H1B Approved Not Stamped Yet - Travelling on Valid F1 Visa

Dear All,
My H1-B(I-129 petition) is approved, as COS , in this cycle and will be valid from 01-Oct-2021 .

My F1-visa & EAD is valid till next year (May-2023 & Jul-2022 respectively).

In this scenario, can I travel to India around July-August and return before 30 Sep 2021 ?

Is there any challenge in this and what all things should I be careful about ?

Can the CBP officer deny entry on F1-visa and ask to enter after Oct on stamped H1B Visa ?

Thanks

To enter on F1 you need a valid reason like being enrolled in college or on OPT job to be more convincing to the IO. If you are already working on OPT job you may be allowed to reenter on F1 visa and OPT EAD.
You need to reenter before few weeks to prove you are back to your OPT job.

I would not advice to travel at this time.

Yes if you try to enter on F1 visa a day before your H1B starts.