H1b to F1 visa stamping

Hello! My H1b is good until Aug 2022. However, I want to go to full time school from Jan 2022. I’m planning to go to India to get F1 visa in Nov. 2021.
I have these questions-

  1. If my F1 visa gets denied, can I come back on H1b visa to continue my job.
  2. If my F1 visa gets approved, can I come back to USA immediately or I can enter only 30 days before start date at I-20?
  3. For some of the past months, I have worked a few hours less than mentioned on my petition (I-129) for H1b. Can that cause any problem?

F1 denial should not impact the existing H1B.

Once your status change to F1, you may only travel within 30 days of your start date on I-20.

This may not be an issue at the time of F1 stamping but may create issues in future if you go back to H1B status or later during the Green Card stage. Again it just depends if USCIS asks for specific details about the hours worked for e.g look at your paystubs etc.

Thank you so much for replying.