Yes, Mexican border for Canadian F-1s is the way to go.

It will likely be many months before you receive the new green card in the mail. Keep on inquiring with USCIS.

I agree, The I-140 couldn't have been rejected or admin closed.

Yes, that should be possible if handled by experienced lawyer.

How can i get a waiver for inadmissible for material misrepresentation in US?

I agree, however, your chances of obtaining a "visitor" visa to the USA are next to nil.

My family member just received her Green Card and it was taken from her at the airport.?

Need more information to be able to provide a meaningful answer.

Filing of H1 after denial of Asylum?Still maintain F1 Visa

Yes, your particular set of facts could complicate the approval of the visa.

Can I apply for Working Visa while in Pending Political Asylum? and can My wife work ?

I agree with my colleagues. As long as you were in valid status when applied for asylum, you will be able to obtain employment based AOS.

Can I add an employer layer on top of my non-profit company to file cap subject H1B? (H1B through Lottery)

Or the employer could petition you through its "for profit" entity, if any.

I applied for my I 751 - I want to travel to Europe - can I travel the the I 797 recipt or do I need to go get a stamp ?

You will be readmitted with your I-751 filing receipt during its validity date. Don't worry.