I need to look for resources regarding application development in Visual Studio using the language C#, the clue given is Arcview ...
That is my post about programming for old ArcView 3.x - [translated by Google to English]:
Programming ArcView 3.x from .NET(C#) via sending Avenue commands to it through the DDE
That is not about embedding maps to your app, but might be helpful. See also other posts on my blog about GIS programming in .NET - there are might be some helpful links for you.