1- Should I max out my contributions to my Roth (this seems like a no brainer)
2- Should I increase my mortgage payments?
I wouldn't. That is prob the cheapest money you will get for the rest of your life. I'd put the extra $100 a month toward investing.
3- I don't know much about investing, so what should I do with the excess? I'm 24 so I can be rather aggressive.
If you don't feel like spending alot of time trying to learn it or taking big risks, I'd say go on Fidelity's site and open an account. Buy into a no fee S&P 500 index fund. If you google it, you will be able to get names. For the most part, managed funds tend to eat up additional gains with fees. Alot of research indicates it might be better long term to just go with an S&P500 index fund.