if you are not in legal status, it would be risky to fly anywhere in the U.S.

Yes, you also need a 212(e) waiver if you were subject to two years home residency, even as a dependent.

if you are eligible to adjust based on marriage and there is any issue at all with your EB visa or adjustment, you should file to adjust based on...

Probably HR would be better. But I expect USCIS would accept a letter from your immediate supervisor, signed, and on company letterhead.

The fact that you filed an application for your wife, as a spouse of a permanent resident, is not a basis to expedite either of the applications. ...

Why do you need to tell them anything? If you can show you need to study English to advance your career, you should be all set.

Either the court will have it, or you can at least get the request for the name change if you FOIA USCIS.

Green cards don't say EB2, there is a different classification system.

It is up to the discretion of the consular post and different posts have different rules.

She cannot do an unpaid internship while in the U.S. on a B1/B2.