What projects can you do? Pretty much anything you want. I started earlier this year, and have a few small programs under my belt. Nothing great, but fun.
Python programs are usually just plain text. They're compiled into a binary form as they're run. It creates a .PYC from your .PY or .PYW. The latter two are plain text, and any of them can be distributed.
To run a Python program, you can run it "python program_name.py" or chmod the program to add execution and just run "./program_name.py". If you are in a file manager, you can set it up so you just double-click it. You can either download a program off the internet, or cut-and-paste into any text editor.
GUI windows can easily be made. Python comes with Tkinter toolkit, but you can get others like wxPython. I've made a few forms for work to analyze some of my data.
www.python.org