It is computer-generated but should be a reasonable estimate.

Yes, you may show a different H-1B approval when you reenter and the CBP Officer will annotate the visa with the new employer's name. I-94 card...

It depends what type of employment authorization you have -- how are you authorized to work now?

No limit as long as you are maintaining your status. If not, then more complicated.

If you know you are moving, be sure to advise this on your cover letter and ask that biometrics, be scheduled in (new location). Also be sure to...

Any future date that does not leave you with a status gap can be selected and USCIS will honor or not.

It is most likely to be rescheduled. No reason to deny unless you have rescheduled multiple times without reason.

If still in status, then re-apply. If not, then explore options through USCIS or Ombudsman to plead your case to reopen as no notice received. If...

Your employer needs the Receipt. Reach out to the Lockbox and/or USCIS to find out where it is if you have courier proof of delivery.

Just be sure to answer truthfully that you do have an immigrant visa case pending and confirm you will leave the U.S. timely at the end of the F-1...