I'm on H1-b, can I work remotely for a company based in UK?

Yes can work remotely as long as it is explained to USCIS.

Name misspelled in RFE Letter

Address this with your wife's attorney. As a rule always be truthful. Use correct spelling.

Can I enter back to US on previous valid H4 visa if my F1 Visa is rejected in Canada?

Absolutely you can return on H4 visa.

I got LPR thru VAWA. My son was under 21 at the time, but I did not include him in the 360 form. Can he retroactively apply?

Had you filed and he turned 21 he would have been fine. Now he will need to file on his own and prove he was abused. Merely being upset at what he...

Typically someone in removal proceeding cannot travel.

My birth certificate is a problem

You can submit alternate documents. Look at that as an alternative.

Do I call consulate of juarez to schedule a interview for a green card

Not sure how you got an appointment before your waiver was approved, but have you filed your DS-260 already?

He will consulate process in Mexico and take about a year.

If someone has been deported and rentered illegally and filed for i 130. Would ICE be searching for that person?

The reason for the deportation is the governing factor and you do not say. With no police problems it is highly unlikely that you are on their...

I94 expiry and I797 validity

Why not just get the I-94 corrected?