Yes, I can generate a new address through the bitcoin-qt command console, but how might I run a for loop to generate 100 different addresses? What kind of file does the bitcoin client take?

You can't. It only accepts specific API commands as described here or by calling the help command in that dialog.

Can I run a python script through the bitcoin command console?

If by the "bitcoin command console" you refer to QT's dialog then no, you can't. You can run a script from your console, though, if you have Python installed in your system or go for a more elegant approach a use a proper RPC API wrapper.

How exactly does sending multiple commands to a command prompt work?

It has already been answer above.

How exactly does sending multiple commands to a command prompt work?

Are you asking about shell scripting in general? If you know how to send one command through the Bitcoin command-line interface, performing multiple commands is just writing a script to do it multiple times - in this case you can't do it at the application level.

Can I run a python script

Yes, use python-bitcoinlib, which is now maintained by Peter Todd, and is available by pip.