Remote job w/o US entry valid H1b

Qs on starting working remotely:

  1. H1b stamped and yet to travel to USA.
  2. Can I start work on remote job while in India?
  3. Have US bank account for salary.

Yes but mind well that the H1B status only applies while you are in the US.

Most employers wont run your US payroll while you are in India (exceptions apply, for e.g. you are working already in the H1B status in the US and then travel to India for few weeks and work remotely, get paid on US payroll) for a case like yours.
Discuss this with your HR and employer.