1. Which one is correct? 2. Is “to” needed before “above”? Thanks.

All of those are fine. No “to” is not needed here.

1. If you're going to say "boost," I would add "up." This course can boost my GPA up to above 3. 2/3. I would say (3) instead of (2.) 2 sounds unnatural. 4. If you're saying improve, it sounds a little weird to put anything directly after it. It would be more like, "This course can improve my GPA. It can bring it up above 3." 5/6. Both sound fine. If you're deciding whether to use boost, bump up, bring up, improve, or raise, it's really a matter of preference and in some cases, formality. For instance, improve is more formal than bump up or bring up. Students talking to their friends might not say improve; they might just say I need to bring up my GPA.

You don’t need “to”. Side note: unless in countries other than the US they use something called a GAP that I’m unaware of, the acronym you are looking for is “GPA”. It stands for “grade point average”