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How to go about it: sync/export data for Accounts from Microsoft Dynamics 365 CRM and show it in a 3rd party web app? Using WS and ASP.NET MVC/C#

I'm trying to get data from Microsoft Dynamics 365 CRM, specifically the Accounts and their data to show it in my own web app that I will build using ASP.NET MVC and C#.
How would I go about doing this so that my web app will instantly be updated when the data in CRM changes? I find it difficult enough navigating through the Dynamics platform already, thanks Microsoft.
The app would work like this:
When run, the app would get the initial data, and establish a real-time connection with WS to the CRM to get further new data/changes.
the app will display this data in a table.
When a change is detected, the web app should update without refreshing the page.
individual table rows will be colored according to number of contacts and if they lack any contact data.
I've started researching webhooks with MS CRM, but it seems Visual Basic is crapping out on me a lot and I cant get the tools to work properly . I think that I have to establish a connection somehow with WebSocket to the CRM, I just don't know which technologies to use and what plugins there are, seeing I'm new to ASP.NET MVC and C#.
Anyway, I just don't know where to start. Could someone send me in the right direction? I would greatly appreciate it!

You can access the data inside a Dynamics 365 / Power Apps instance (also known as Dynamics CRM or Dynamics 365 CE) using the APIs provided by the system.
You can leverage these APIs using the SDK provided by Microsoft (this one https://www.nuget.org/packages/Microsoft.CrmSdk.XrmTooling.CoreAssembly/ or this one in preview for .NET Core https://www.nuget.org/packages/Microsoft.PowerPlatform.Dataverse.Client/) or by calling the API directly inside the language of your choice.
Usually you need to deal with CRUD events, and the APIs can do that. In your question you mention "the web app should update without refreshing the page" so you will need to take a look at webhooks (here a doc page https://learn.microsoft.com/en-us/dynamics365/customerengagement/on-premises/developer/use-webhooks) handle them in your application and see if they fit your requirements.

Dynamics 365 CRM SDK or Rest API

I need to create a CRM E-Mail activity with attachement from code. As far as I know there are two ways to do this. I could use the dynamics 365 CRM SDK or the dynamics 365 CRM Rest API. My question is which one I should use at the moment? I know Microsoft has many good API, but many of them seemed unfinished to me. Can you guys help me out?

I've you're in the .Net Framework, always use the SDK. It hasn't really changed since 2011, and they are slowly porting the calls over from the SOAP endpoint to the WebApi for you, with no work on your end.

If you are doing integration from outside CRM, I would recommend WEB API which is the cross-platform RESTful solution going forward. Before 8.x CRM version - SDK was the only option available (still you can use it today).
The keywords are important, you can find lot of community blogs for code samples & better documentation. You can setup Postman & test the web api endpoints, even you can use CRM REST Builder for development purpose.
Endpoint: <your instance url>/api/data/v9.1/emails
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Create Email using web api
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I need to be able to upload a document created totally outside Sharepoint and CRM into the CRM document management system on the associated Sharepoint site. By the way it is Microsoft Dynamics CRM online. I have searched high and low, asked Sharepoint experts, called Microsoft Support but cannot find a solution. The document is created dynamically, probably in some sort of batch process, so this needs to be handled programmatically. The application is written in C# and I want, after creating the document, to find the relevant Sharepoint folder within the CRM system, which will be under one of the account entities, and upload it there. The one solution I did come across is this:
Add document sharepoint using web service Microsoft Dynamics CRM
Which seems promising but I can't get it to work. Has anyone ever done anything like this before?

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Microsoft provides a PowerShell command Get-Msoluser to retrieve all office 365 users. I don't want my application tied to PowerShell, so I want to write a C# function to do the work, unfortunately, there's not much information on this topic.
I looked in the Office 365 APIs Preview documentation, no such functionality; also I looked into the SharePoint Client Object Model, no such thing either.
Can this be done without PowerShell? Is there a SDK can do this?

Yes, you can use the Azure AD Graph Client Library. There are also a couple of samples in that link that will show you how to retrieve your user(s).
This library is available as a nuget package.
https://www.nuget.org/packages/Microsoft.Azure.ActiveDirectory.GraphClient/1.0.2

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A customer is moving their solution to a "private cloud", that is partner hosted using ADFS 2.0 and claims based authentication only. However, they have an application that each month generate reports for each account and sends this as Excel-attachment to several CRM contacts. The problem now is how to generate the reports automatically by code?
With AD deployment it is possible to contact the Reporting Services-service directly to render reports (to excel, pdf etc). But how can I do this with CRM 2011 and ADFS? It will be possible for me to get access to reporting services through the use of VPN but what about authentication? Also, how would customers that use Microsoft Online solve this?