Does Screen Printing Require A Heat Press?

You don't need a heat press to screen print. A heat gun will cause you more problems than it's worth. I would suggest getting a flash dryer.
Simple Green will not remove emulsion. The best way to save money there, is to make sure you're using a good emulsion remover that works. Simple Green can be used as a degreaser though.

If you already have a heat press, then yes, I would use that to cure shirts. It would be way better than a heat gun and an iron would not work.

I mean do neenah print at home transfers last, work, and look decent or am i better off sticking to screen printing?

I guess I answered my own question with that one i'll stick to screen printing, is the heat press better then the heat gun even for the water based inks?