There's no need to concern C# in Android even the server is written in C# as the websocket protocol can be implemented in any programming language.
Besides of your learning materials, if your server should be written in C# and Android have to connect to it, shortest path to achieve is to use SignalR project.
check out SignalR Project link (http://signalr.net/)
SignalR use WebSocket as main protocol and http long-polling technology as a fallback. And, Android library named SignalA is supported also. I tested it and was happy to use it last year. The fallback(long-polling) is important as Android does not support WebSocket protocol in all versions.
If long-polling is not your option (it can consume cellular data plan more than expected), then you can try to create your own communication rule with raw WebSocket protocol, For that, use Java-WebSocket project in Android and many C# libraries are introduced in CodeProject.