There is no way to give you the path of the stones and say: "do this, this and more and you will have everything you need", until I find it strange the question has no vote to be closed as too wide or mainly based on opinions.
But anyway, I know what it’s like to be in a situation like this and I’ll try to help you in a very succinct way around here, as you develop, specific doubts will arise and then we can help you better.
Reinforcing: I’ll give you some tips, it’s not rule or anything.
How can I do that?
You think ahead and start making a REST API. Making the API to handle your data model, etc. Then you can use it in any application you are developing, whether desktop, web or mobile.
Develop the site on ASP.NET and then create the app on android?
This will depend on your taste, need and other factors. If you’re going to follow the idea of creating an API, I think it’s interesting to develop the API first. But, again, that’s not the rule.
I found Xamarin, I saw that in it can develop to cross Platform, but would not be limited development?
Limited in what way? Xamarin is very good, you develop everything in C# and da deploy in a (virtually) native app. Not to mention all the tools that are available such as Xamarin Insights and Xamarin Test Cloud. But of course all this is paid.
I think reading these questions will help you a lot.
What is REST and Restful?
Web Service Type Differences: SOAP, REST, XML
Webservice REST Simple