Connecting HTML5 to backend

[PeejAvery]

I want to create a program in HTML5, but I need also to have a backend which will handle all the logic.

You would have to HTML5 is still limited in many ways since not all features are supported yet. HTML5 itself is a standard in progress...not fully proposed.

Can I connect a backend which is written in C# or in Java to HTML5? if so how?

You could use PHP, Java, RoR, Python, PERL, ASP classic, ASP.NET (C# or VB.NET), etc. You have plenty of options for the backend. However, what you use will depend on what your web host server runs.

My program needs also to handle reading and writing to xml files. I guess that the backend will need to handle this task, but can the HTML side handle it as well?

Client-side scripting (JavaScript) cannot read/write to the client disk. This would be a major security hole if that existed. All file operations will need to be handled by the server-side. The only writing you can do is to localStorage for offline database handling.