Can an Indian citizen(H1B visa holder of USA), whose I-140 is approved, start a pvt. ltd. company in India?

Can an Indian citizen, who is an H1B visa holder in the USA, whose green card is under process (I-140 approved and waiting for priority date), start a pvt. ltd. company in India?

Also when such person starts a pvt. ltd, he/she will be director of firm. He may not be getting salary though. Is this allowed?

If your business is limited for India only, it doesnt matter about your US immigration (at least till i140).

All you need to do is to comply with US immigration guidelines for your H1(i140 is for a future employment, you dont need to satisfy any(except your professional eligibility) conditions of your i140 future employment.

Yes you can. even with your Greencard under process, you are a PIO (person of an Indian origin)