So I've been entering the world of Python just recently, and directed it to quick, personal programs made for myself and professional use for web application design with Django. I've taken a few introductory Python tutorials and most Django tutorials, and have been reading Python documentation whenever possible.
I've recently seen that .pyc files are just bytecode (compiled) .py scripts, and don't make the Python language any faster, only lighter and non-human-readable. However, in a medium-low traffic site (let's say, 95% of web sites), this is negligible in difference from PHP, for example (and I find Python to be thousands of times more productive).
The question is: can you execute Python programs from .pyc files where there is no .py file? If yes, is this also possible in Django? How? Is it a good way to make web apps "almost closed source"?
can you execute Python programs from .pyc files where there is no .py file?

Yes. Simply place the .pyc file wherever the .py file would normally be used (except into your text editor, of course).

If yes, is this also possible in Django? How?

No difference. The interpreter handles the files the same way regardless of what framework is being used.

Is it a good way to make web apps "almost closed source"?

Not really. Decompiling compiled Python bytecode is trivial.
Run compiled Python