So I looked through the rules and there was nothing against Parsec for 2P speedruns, is that allowed or do we both have to be in the same room to do it?

Parsec IS allowed for doing runs.

Thank you! I wanted to make sure before we did a run!

I have another question about swap mode...

What are the rules on 1 player 2 controllers (1p2c)?

You have to submit it to "Swap Mode 2P", since you are using 2 input devices for playing the game.

Other than that, just follow the rules.

Steam remote play worked better than Parsec in my opinion.

yeah but when we tried SRP it was so laggy it was insane but parsec was fine