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How to keep canvas a fixed size while stretching its container

I am trying to make a really simple editor for images. Since the control panel is showed right next to the Canvas, I'd like to put a border between them (I am open to suggestions like a GridSplitter though). I have the Canvas nested in a ScrollViewer nested in a Border. When the image loads in the Canvas, if I resize the window I the image resizes with everything else. Since I am editing this image, I'd like to keep it to its original size and, if the Canvas is to big, use the ScrollViewer to handle that. I don't know if it is more recommendable to put the border around the Control Panel instead.
XAML Code:
<Border BorderBrush="Black" BorderThickness="2" Grid.Column="2" Grid.Row="0" Grid.RowSpan="10" Height="Auto" Width="Auto" HorizontalAlignment="Stretch" VerticalAlignment="Stretch">
<ScrollViewer x:Name="canvas_RosetteMap" Height="Auto" Width="Auto" VerticalScrollBarVisibility="Auto" HorizontalScrollBarVisibility="Auto">
<Canvas Grid.Column="2" HorizontalAlignment="Center" Height="Auto" Grid.Row="0" Grid.RowSpan="10" VerticalAlignment="Center" Width="Auto"/>
</ScrollViewer>
</Border>

You should use a Grid instead. Canvas are not good at handling resizing, scrolling or anything like that. Here is a simple example that should work with an Image also:
<Border BorderBrush="Black" BorderThickness="2" HorizontalAlignment="Stretch" VerticalAlignment="Stretch">
<ScrollViewer x:Name="canvas_RosetteMap" VerticalScrollBarVisibility="Auto" HorizontalScrollBarVisibility="Visible">
<Grid Width="Auto">
<TextBox Background="Beige" VerticalAlignment="Top" HorizontalAlignment="Left"/>
</Grid>
</ScrollViewer>
</Border>

WPF ScrollViewer is not working

I want to add scroll view to my program and I tried ScrollView control but that don't take effect. It's my first time dealing with scrolls please help me :).
My xaml Code:
<DockPanel Grid.Row="1" Background="#FF695887">
<ScrollViewer VerticalScrollBarVisibility="Auto" Height="795">
<Canvas Name="zemelapis" Height="Auto" Width="Auto">
<Image Name="pav_kelias" />
<Image Name="car1" />
</Canvas>
</ScrollViewer>
</DockPanel>
Because these 2 images is not fitting here I need a scroll for them. Maybe I should use ScrollBar?
My program example: https://gyazo.com/a4ba7e4d5004632e2229a87e686c4c09
, as you can see bottom image is not fitting in range of window.

You have specified Auto as Height and Width. This implies that the Canvas will fill the height available to it.
From the documentation:
Auto sizing behavior implies that the element will fill the height
available to it.
In this case the available height is the height of the ScrollViewer.
If you want the Canvas to be bigger, and hence the ScrollViewer to scroll, you should set a height on Canvas that is bigger than the height of ScrollViewer.
So, for example:
<DockPanel Grid.Row="1" Background="#FF695887">
<ScrollViewer VerticalScrollBarVisibility="Auto" Height="795">
<Canvas Name="zemelapis" Height="1000" Width="Auto">
<Image Name="pav_kelias" />
<Image Name="car1" />
</Canvas>
</ScrollViewer>
</DockPanel>

If you want your ScrollViewer to work easily, use a Grid instead of a Canvas:
<DockPanel Background="#FF695887">
<ScrollViewer >
<Grid Name="zemelapis">
<Image Name="pav_kelias" Source="acteurs.png"/>
<Image Name="car1" Source="public.jpg"/>
</Grid>
</ScrollViewer>
</DockPanel>
As explain by Domysee, Canvas gives you total control of the layout. Grid however will automatically adjust its size depending on the content.
See http://www.wpf-tutorial.com/panels/introduction-to-wpf-panels/

Centering a mediaelement according to the aspect ratio

So, I've got this mediaelement, which I want to appear in the middle of the screen, 20 pixels away from each edge, and when it's width gets to 600, it stops expanding and stays where it is. I've got the following XAML to get exactly what I want:
<Grid x:Name="video">
<MediaElement x:Name="player" AreTransportControlsEnabled="True" Margin="20,0" MaxWidth="600" HorizontalAlignment="Center" VerticalAlignment="Center"/>
</Grid>
The only problem is that the VerticalAlignment property seems to always be set to "Stretch". How can I fix this? I've tried using a viewbox, which works flawlessly, except I then get overly large or small TransportControls. I've also tried putting the mediaelement inside another grid with centered alignments, but I still get the same problem.

What you want is
20 pixels away from each edge.
But in your code you defined Margin="20,0", if you read the FrameworkElement.Margin property, you will find the useage <frameworkElement Margin="left+right,top+bottom"/>. With your code, this usage makes your MediaElement stretch in the vertical orientation.
If you use the Live Visual Tree to get a real-time view of your running XAML code, you will find, when you use the code Margin="20,0", the MediaElement is like this:
And if you use the code Margin="20", the MediaElement is like this:
The dashed red border in each picture stands for the MediaElement control.

<Grid Background="{ThemeResource ApplicationPageBackgroundThemeBrush}">
<Pivot Margin="0,0,0,0" Background="LightGray">
<PivotItem Header="Formulas">
<Grid>
<GridView HorizontalAlignment="Stretch" HorizontalContentAlignment="Center" Background="#FF983636">
<GridView.ItemsPanel>
<ItemsPanelTemplate>
<VariableSizedWrapGrid Orientation="Horizontal" />
</ItemsPanelTemplate>
</GridView.ItemsPanel>
<x:String>One</x:String>
<x:String>Two</x:String>
<x:String>Three</x:String>
<x:String>Four</x:String>
</GridView>
</Grid>
</PivotItem>
</Pivot>
</Grid>
The key here is HorizontalAlignment="Stretch" on the GridView.
The HorizontalAlignment="Center" on the VariableSizedWrapGrid inside the ItemsPanelTemplate inside the Gridview; should do the trick which will always keep the content centered regardless of the width of the screen.

In the end, I found how to fix this, by keeping a constant aspect ratio of 16/9:
XAML:
<Grid SizeChanged="player_SizeChanged" Background="Black" HorizontalAlignment="Center" VerticalAlignment="Center" MinWidth="1" MinHeight="1" Margin="30" MaxWidth="1000" ScrollViewer.VerticalScrollBarVisibility="Disabled">
<MediaElement x:Name="player" Margin="0">
</Grid>
C#:
private void player_SizeChanged(object sender, SizeChangedEventArgs e)
{
(sender as Grid).Height = (e.NewSize.Width * 0.5625);
}

Fill StackPanel inside DockPanel

This should be easy: how can I stretch StackPanel inside the DockPanel, so that it would fill the whole parent's content and also maintain it's HorizontalAlignment?
Example:
<DockPanel LastChildFill="True">
<StackPanel Orientation="Horizontal" HorizontalAlignment="Center" Background="Yellow">
<Button Height="30">Button1</Button>
<Button Height="30">Button2</Button>
</StackPanel>
</DockPanel>
In this example the StackPanel's width is the same as the combined width from both buttons (and the background here is yellow), but the remaining space in DockPanel stays white. Looks like the LastChildFille property isn't working in my example.

I think by setting HorizontalAligment to Center on the StackPanel you are overriding the behavior of the DockPanel to fill the whole space with the StackPanel.
When i understand your question right, you want that the full space is yellow and the stackpanel with buttons is centered in the middle. Then you should wrap the StackPanel inside a Grid.
<DockPanel LastChildFill="True">
<Grid Background="Yellow">
<StackPanel Orientation="Horizontal" HorizontalAlignment="Center">
<Button Height="30">Button1</Button>
<Button Height="30">Button2</Button>
</StackPanel>
</Grid>
</DockPanel>

WPF Create a slide out panel

I don't know how this works technically but my requirement is as follows. I have a DataGrid and to input data into the DataGrid, I want a panel at the bottom of the DataGrid that slides out on a button click showing input options. Except, as the panel slides out, the DataGrid has to resize vertically as well. Can someone throw some light on how I can implement this?

You should be able to use a StackPanel with 2 children, your grid and your panel. Set the initial height of your panel to 0. Once the button is clicked, set the height to whatever you need it to be (e.g., MyPanel.Height = 20). You might want to wrap the grid in a ScrollViewer in case that is needed.
<StackPanel Orientation="Vertical">
<ScrollViewer Height="Auto" VerticalAlignment="Stretch">
<Grid Height="*" VerticalAlignment="Stretch" />
</ScrollViewer>
<ContentControl x:Name="MyPanel" Height="0" />
</StackPanel>
You might need to experiment with VerticalAlignment and Height="Auto" or Height="0" to get the layout you want.

You can use Expander. Please look at the following code snippet.
<DockPanel>
<Expander DockPanel.Dock="Bottom">
<StackPanel>
<TextBlock Height="25"></TextBlock>
<TextBlock Height="25"></TextBlock>
<TextBlock Height="25"></TextBlock>
</StackPanel>
</Expander>
<Border BorderBrush="LightGreen" BorderThickness="2">
<DataGrid/>
</Border>
</DockPanel >