Unless you are in legal status, options to change to work categories are limited even with a sponsor. If you have less than 180 days out of...

90 days before February XX, 2025 assuming otherwise eligible.

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CBP guidance is 180 days in a year; but they will need to be convinced there is no unauthorized employment while here and you need to be upfront...

If the individual is not eligible for automatic or derivative citizenship, then the normal route is to first apply for permanent residency.

You can get an I-20 from the school but will need to get an F-1 visa at the consualte.

This is not a process for citizenship it is for permanent residency and i strongly recommend you not try to do on your own.

No reason you can't do that one residential address and one for mailing.

Yes, you are not required to work to be eligible for citizenship. With regard to taxes, you need to pay what you owe only.

Did your son come legally to the U.S.? If yes, your current spouse can file for your son as his stepson (marriage before he is 18 years of age)...

He can get a DS-2019 for you in the J-2 category.