Since you are going to use Web API, why are you confusing yourself to use native .NET framework at all?
You should build a simple Android application with default WebView control added to it. Which can then target your API. Do you know much about
ASP.NET Web API[
^]? If not then please learn it there. You should also have enough understanding of routing in ASP.NET Web API; it is just a little different from ASP.NET MVC Routing.
Then, you can pass your data from Android application. In your application store all of the data that you want to send to your Web API. While creating the routing make sure you create an efficient routine scheme which would let you upload the data. On the Web API use Entity framework to commit all of the changes to your database. There is no need to involve native .NET framework's procedures, just stick to the Web API in this case.
Also there is only SQL Server database, there is no .NET database.