1) Can each web-app use the same database?
2) Can each web-app use the same static and media settings, working directory and WSGI configuration file?
Yes, apart from the WSGI file -- you have to deploy each web app via the Web page, which will result in creation of a separate wsgi file for each of them. Contents of those files can be the same, though.
3) Can each web-app refer to the same source code folder?
4) If the above questions are answered with yes can you think of any potential problems running multiple web apps with the same resources?
The major issue that comes to my mind is the database state -- depending on what your apps are doing, you should probaby consider if there would be no clash in data (e.g. users trying to create an account with the same handle on different sites).
5) Sites framework is a standard core part of Django. Will PythonAnywhere support Django applications including the Sites framework by allowing multiple domains for each web-app in the near future?
No, we're not planning to change the way we treat domains on PA right now.