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Using ViewModels in ObservableCollections in Prism

As far as I know, the default way to use a ObservableCollection that is bound to a listview is with model classes as elements (ObservableCollection<MyModel>). So when a listview element is selected, we use NavigateAsync and pass the model, which then can be used by the ViewModel to "fill itself".
The problem with this approach is, that it's not possible to use ViewModel properties for binding in the listview.
For example:
I have a View, ViewModel and Model "PickList", which contains a collection of "PickLine" objects - each having a View, ViewModel and Model themselves. The PickLine object contains a property "PickedQuantity" and a property "OpenQuantity". Now in my PickList view, I don't want to bind these two to separate items (e.g. two labels), but I want to have one label to display both I a format like for example "PickedQuantity / OpenQuantity". I know this example can be solved by using multi binding or something like this. But that's not the meaning of it all.
My PickLine ViewModel already has a property "QuantityString", that I want to bind to the label of a listview element via DataTemplate. But how can I do this. Is it even possible?

Make a property that combines the two other properties and bind to that. E.g.:
public string FullQuantity {get {return $"{PickedQuantity} / {OpenQuantity}";}}
Then in the setter for PickedQuantity and OpenQuantity, you will want to call whatever PropertyChanged method you have set up to notify the bindings of a property change and pass in the FullQuantity property name so elements that are bound to FullQuantity get updated when either PickedQuantity or OpenQuantity are changed.
This way, you are only binding one label's text to one property and that label would get updated when either of the two quantity properties are changed.
Note: I am unfamiliar with Prism, but this approach should work regardless of the Mvvm framework in use.

Your PickListViewModel should expose a collection property whose items are of type PickLineViewModel (not PickLine).
Whether you need an ObservableCollection<PickLineViewModel> depends on where changes can happen - in service / model that initially created the PickLines or in the GUI or both. In any way, you have to make sure the changes are propagated from one side (the collection of view models) to the other (the collection of models). Google wrapping observable collection as a starter (hint: avoid two-way sync if possible). These blog posts are old but still relevant and make a good reading. A trivial wrapping is described in this answer.

WPF MVVM Change Model

I have a UserControl where the data gets passed in via a dependency property.
The UserControl is backed by a view model and the data is assigned to a property of the view model.
The XAML binds to both properties in the view model as well as properties within the passed in data.
The problem is if the user changes the data then databinding with the UI breaks. The UI is still bound to the original data object.
How can I cause the binding to get refreshed? INotifyPropertyChanged is implemented throughout, but it is not the property that is getting stale, but the binding. Basically, how do you go about replacing a backing model?
Since I'm not sure my description is clear I will try to describe it again in pseudo code.
<MyControl Source="{Binding Data}"/>
Where source is a dependency property of MyControl. In the PropertyChangedCallback this data is handed to the view model.
MyViewModel.Data = Source;
Within the MyControl XAML things are bound to this model.
{Binding Path=MyViewModel.Data.Item}
If you are wondering why the dependency property is defined in the UserControl, it is because it is a reusable control and the end user should not know about the view model.

"The UserControl is backed by a view model" and thus breaketh the application.
The UserControl's DataContext should be the Model. Period. If you need to perform UI logic, do it in the codebehind. Need something else? Create DependencyProperties on the surface of your UserControl to supply them.
When you create a ViewModel specifically for your UserControl, you break the natural flow of the DataContext (at this point, probably the Model the UC is designed to work with) and binding within the UserControl. It's pointless in most cases and harmful in some (as you have noticed).
My canonical answer on the subject contains more details.

Are you trying to swap-out the DataContext of the usercontrol during an application's session?
If you are, then I am fairly confident that this will not work.
Have you considered spinning up a new instance of that user control with the other DataConext?

How can control in the view get specific data from view model?

I have multiple of views (user controls), each with its own ViewModel. To navigate between them I am using buttons. Buttons display image and text from corresponding view model and also need column and row (because there are like 10 views: 10 columns with different number of rows each).
Right now buttons are created dynamically (I made a Navigator control for this) and for view models I have base class to hold text, image, column and row. Number of views available will be different (depends on user level and certain settings), that's why it's I need control here.
Question: how shall my control get data from view models?
Right now I have interface INavigator, defined in (lol) control itself. And view models implement it. I could go opposite, let my control to know about view models. Both looks wrong.
There is a single Navigator control what has, lets say, Items bound to a list of view models. It can cast each view model to INavigator or ViewModelBase (common for all pages) to obtain specific view model image, text, column and row. So either view model knows about control (to implement INavigator) or control knows about ViewModelBase.. And this is a problem, both solution bind tight control and view models, which is bad in mvvm.
Schematically

The way you've drawn your diagram answers your own question as to how you should structure the code for this.
What you need is one VM (let's call it MainVM) which contains an ObservableCollection<VMBase> of the other VMs (using your base type so that they can all happily live in the same collection).
Your View needs an ItemsControl (bound to your ObservableCollection<VMBase>) where you specify a DataTemplate for the Button using the properties exposed by the VMBase type only. Set the Command property in the Button to call SwitchCommand, CommandParameter is set to the item itself (i.e. {Binding .}).
Your View also needs a ContentControl bound to a SelectedVM property on MainVM which you can populate.
Implement SwitchCommand to set the SelectedVM property based on the value from the CommandParameter.
public void ExecuteSwitchCommand(object parameter)
{
var vmBase = parameter as VMBase;
if (vmBase != null)
SelectedVM = vmBase;
}
All properties mentioned here should be INotifyPropertyChanged enabled so that the View registers when they change and updates the UI.
To get the different UIs for the ContentControl, add type-specific DataTemplates for each of your specific VM types to the Resources file of your View (or if you're smart and are building a custom plug-in framework, merge the Resource Dictionaries).
A lot of people forget with MVVM that the whole point is that there is a purposeful separation of View from ViewModel, thus meaning you can potentially have many Views for a single ViewModel, which is what this demonstrates.

I find it's easiest to think of MVVM as a top-down approach... View knows about it's ViewModel, ViewModel knows about its Model, but Model does not know about its ViewModel and ViewModel does not know about its View.
I also find a View-first approach to development the easiest to work with, as UI development in XAML is static (has to be).
I think a lot of people get to wrapped up in 'making every component (M, V, VM) standalone and replaceable', myself included, but I've slowly come to the conclusion that is just counter-productive.
Technically, sure you could get very complicated and using IoC containers, create some ViewLocator object which binds a View-type to a ViewModel-type, but... what exactly does that gain you besides more confusion? It makes it honestly harder (because I've done this at one point) to develop because now you've lost design-time support first and foremost, among other things; and you're still either binding to a specific view model interface in your view or creating the binding at run-time. Why complicate it?
This article is a good read, and the first Note: explicitly talks about View vs. ViewModel. Hopefully, it will help you draw your own conclusions.
To directly answer your question, I think having your ViewModels implement an INavigator interface of some sort is probably ideal. Remember your VM is 'glue' between your view and model/business logic, its job is to transform business data into data that is consumable by your views, so it exists somewhere between both your UI and business layers.
This is why there are things like Messengers and View Services, which is where your navigator service on the ViewModels can fit in nicely.

I think the design has led to a no way out situation.
I believe that creating a custom button control where the dependency properties tie the image, the row and column actually provide a way for the page, which it resides on ,to get that information to them; whether they are dynamically created or not.
Continuing on with that thought. There is no MVVM logic applied to a custom control, the control contains what it needs to do its job and that is through the dependency properties as mentioned. Any functionality of the button should be done by commanding; all this makes the button data driven and robust enough to use in a MVVM methodology or not.
Question: how shall my control get data from view models?
There should only one viewmodel which is the page the control resides on. The control is simply bound to information which ultimately resides on that VM. How it gets there, that is up to the programmer. If the button is going to contain state data, that is bound from its dependency property in a two way fashion back to the item it is bound to.
By keeping VMs out of the buttons and only having one VM that is the best way to segregate and maintain the data. Unless I am really missing something here....

Same as others here I find it a bit hard to actually understand what you are asking, so this is quite general. The answer to the question header is simply: the Control gets the data from the ViewModel through bindings, always. You set the DataContext of your Control to the corresponding ViewModel, and from there you keep the ViewModel and the Control synchronized:
If you add an ItemsControl containing buttons to the View, you add an ObservableCollection<ButtonViewModel> to the ViewModel and bind the ItemsSource of the ItemsControl to this.
If you allow the user to dynamically add content to the View, the actual code that does it resides in the ViewModel, e.g. when the user clicks on a button "Add Button", you use the Command property to call a ViewModel method that adds a ButtonViewModel to the collection and the View will automatically reflect your changes.
There do exist complicated cases that are impossible to code exclusively in the ViewModel, I have found Behaviors to be the missing link there, but I'll get into that when you show me the specific case.
If you'd like to get a working example, please provide as much code as you can, with your exact expectations of what it should do.

MVVM how best to display ListBox.SlectedItem

I have a ListBox bound to a list of ViewModel objects on the LHS of my screen. The ListBox.SlectedItem is bound to a property on my "MainWindowViewModel", called CurrentItem. On the RHS I have a large area that displays the selected item in detail, containing many nested controls for editing and browsing the information the ViewModel contains.
There are two approaches to building the view that I am aware of.
The large area on the RHS is a ContentPresenter with the Content property bound to CurrentItem. In my resources, define a template to be used with my ViewModel object.
The large area on the RHS is a fixed UserControl containing all the required xaml to display the my ViewModel. I bind the DataContext property of my UserControl to CurrentItem.
Which is the nicer approach and why? Perhaps option 2 is better in general but option 1 could be used when there are view models of different types in the ListBox, each with their own template?

Personally I would not bind directly to the selected Object in the ViewModel because doing that you are breaking the MVVM Pattern.
What I would suggest to do is to create a ViewModel for the whole view Including your list of ViewModels and adding a SelectedViewModel Property that is bound to the selected item. So the selection infromation is also in the ViewModel.
Then you can bind the SelectedObject of the "parent" ViewModel to the RHS.
I would suggest reading this MSDN Article for an introduction how to display SelectedItems using the MVVM Pattern.

How to move IsSelected for MVVM out of the business objects?

I have a reasonably large application in C#/WPF made with MVVM (sort of).
In listviews I use the IsSelected bindinded to the selected items. These IsSelected property is located in the model of my app, not in a ViewModel.
Currently I only have one viewmodel pointing to one list in the business object (model, not view model), but in the future I possibly want to change this and than the IsSelected property inside the model is not possible anymore (otherwise both ViewModels would have the same selected items).
The selection mode is multiple and can range between 1 to 128 (max length of list) items.
I think it should be inside the viewmodel somehow, but how should I achieve this?

When using MVVM, you are not restricted to a single view model. Yes, you might expose parts of your model from your view model, but you can also expose other view models.
In this case, I'd recommend wrapping the instances of the collection in their own view model and set the binding root for your item templates to that.
For example, if you were data binding to a collection of models, you could pass the instances of each of those models to a view model that wraps the model and then exposes the IsSelected for binding on the view model.