Yes, you should not file and then plan to leave the U.S. for two months.

You can apply. It's usually much faster to consular process, but currently, under the COVID world, changng status in the US may be preferable.

Sure, but your departure automatically withdraws your application for an extension of status.

If your green card has not expired, and you are eligible for citizenship, you can file for citizenship.

Correct, a visa to bring a fiance to the U.S. is a K1 visa.

The fact that you filed a downgrade does not change the analysis. If you do not maintain your H1b, then you will have to stop working during any...

You can certainly try. A lawyer could help you file the application.

No, self employment is not permitted on a visitor's visa.

Your prior alleged violation does not bar you from getting a tourist visa.

It is possible but not likely, since you have proof you were admitted as an H1b.