Am I eligible to travel on AVR to Mexico and reenter US?

Hello!
I am planning to go to Cancun, Mexico for 5 days in may.
My visa stamped on passport is expired and my i94 on the cbp website is also expired But i have renewd h1b and have valid i797 till dec 2023.
I renewed my passport last month. So new passport is blank. And, old passport has expired visa stamped.

  1. Am I eligible for Automatic visa revalidation?
  2. Do I need Mexican visa to travel to Cancun?
  3. What documents do I need to reenter US?
  4. Is it recommended to use AVR in my case? Or, go to India for dropbox appointment in April ( I already have booked an appointment for April 13th) but I will cancel if I can get some confirmation that AVR gets approved without any problems .

Thanks Anil. Do you know the answer to question 2?

You can visit Mexico with a valid US visa in the passport.