If your O-1 Petition is denied this should not affect your future ability to apply for ESTA unless the Denial was for fraud or similar matter. ...

yes as long as you have a valid I-20 and are attending school you are legal to remain here whether the visa has expired or not. The first time you...

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This should not be a problem especially since you are not working there after April 11 i assume.

impossible to answer without knowing the details of the fraud they claim you committed.

I concur with Evelyne but this is a risky strategy as you will have no status and no right to work while waiting for that U.S. citizen to pop into...

same thing -- just a form response probably referring to your medical exam

I recommend a Reentry Permit to avoid hassle at the border. I am sure you are aware this will delay the date of your eligibility for citizenship...

don't overstay. You can contact CBP for an extension with the medical evidence.

if counted in the last 6 years then you would not be subject to the lottery with the new H employer.

Yes you may have a new employer file an H-1B (that way you can port immediately and begin working upon receipt of the I-129 H-1B Petition) and PERM...