I won't recommend Xamarin as a game development engine, because just to make things work in Xamarin, you are again going to ask for help from another tool.
Instead, I would recommend that you get a game development engine. Unreal, Unity or any other, doesn't matter. As long as that framework supports Android, it would do the job. Unreal and Unity do support C#, Unity supports it natively whereas Unreal uses Mono for development because it is a C++ based engine.
Anyways, read my previous answers that may help you to get started in this.
Tutorial in Game Development[
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Selling items in Android Game[
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How to animate a charater in Unity 3D (running game)[
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Need help in android development[
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