The grace period is not for exiting/reentering so, on that basis, no. You should be able to reenter as a Canadian, without a visa, for "cleaning...

Can I re-enter US if I asked for early authorized withdrawal on my F1 visa?

The grace period is not for exiting/reentering so, on that basis, no. You should be able to reenter as a Canadian, without a visa, for "cleaning...

Both the H-1B and I-140 petitions belong to the employer, not to you. You should consult with your employer's immigration counsel and fully reveal...

Does early authorized withdrawal affect adversely my future entry?

There are many information gaps in your question. Please hire qualified immigration counsel to provide specific guidance.

I-601A, consular processing, and reentry is your only way to obtain GC-based work authorization. As an EWI, you cannot adjust; no stateside cure...

Deported 10 years ago and banned for 20? Please hire experienced immigration counsel for specific guidance.

This requires much more information, particularly re: the E-2 expiration and PERM filing/priority dates as well as your ultimate immigration goals....

Passport and backsupport

Your nearest country consulate / passport office may be willing to discuss this with you.

Filing VAWA petition with USCIS when a person has a prior?

Best practice: Do not proceed with filing until hiring an experienced immigration attorney to assist you with the petition.

Make payable to "U.S. Department of Homeland Security" with yourself ID'd in Memo area of M.O.