Very likely you can. There is an exception to maintaining lawful status, that as a matter of discretion applies when you file for asylum while...

You could qualify for an E2 visa as a treaty investor. You would not be permitted to do other work on the side as an E2.

A clearance from the county sheriff would very likely qualify as a police clearance letter.

You can file to "recapture" your two months.

I don't see why you could not do that since even the same school has to keep updating it's I-20.

No, there is no "grace period" after a person turns 21, to file a visa petition for him as a minor. If he gets a work permit [EAD], then yes, he...

Either location is fine. You can enter with a visa in your old passport, in which at the airport they will stamp your new passport.

If USCIS granted your mother's form I-485, then she is a lawful permanent resident. If she never filed an I-485 she may wish to do that.

It seems to me that your wife will be getting the profits from the business, so inevitably you will be getting a financial benefit from your work. ...

No, but heads up, tomorrow the new regulations on public charge grounds of inadmissibility will be published.