Do I have to have my splits with the run like on screen or is it okay if I stream it on twitch and not have splits???v

You don't need splits.

Okay to not have splits, but make sure that your run time can be verified, so the video can't have missing parts and such (like twitch picnics). Splits are only there for decoration anyways, for the most part.

Can you record and stream at the same time using obs??

When you're running the game with one monitor how do you manually split on live split?

I assume you got your answer to this, but you should run it in windowed mode and bind the keys to whatever they are for splitting. Or just download the autosplitter.