The first step is to go through a beginning level Web API tutorial so you understand the basics.
You also want to learn how to use HttpCleint to make calls from the xamarin application to the Web API application.
https://learn.microsoft.com/en-us/dotnet/api/system.net.http.httpclient?view=net-6.0
https://learn.microsoft.com/en-us/xamarin/xamarin-forms/data-cloud/web-services/rest
should i recreate the models folder in the new application ?
It depends on your application requirements. Usually you'll end up models in both projects. You could also have a separate class library project with shared models. Again go through a few tutorials.
how to insert the firebase connection in the new application?
Read the firebase documentation. Firebase has an SDK for .NET.