Typically, you'd have something like a web service on the receiving end of things. If you definitely want to use a WinForm app, you probably want to use a TCP client and server. If you're new to programming, this will not be trivial, especially when communicating between two different technology stacks.
For the C# side, you'll probably want to set up a
TcpListener. This won't answer all of your questions, but it will get you started:
TcpListener Class (System.Net.Sockets) | Microsoft Docs[
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For the Android side, this should get you started:
Sending and Receiving Data with Sockets · codepath/android_guides Wiki · GitHub[
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If you don't already have the knowledge, you'll need to learn about sockets communication and make sure that your firewalls / permissions are set up (on both sides) to allow the communication.
Another option you can explore is WCF, though not sure how well this will cooperate with Android, which is why I mention it last.
Hello World, Basic Server/Client Example of WCF[
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