General Nonimmigrant Visa

I came to US on H-4, so I have only H-4 stamping in my passport. Got my H1b picked up in lottery two years back, and did COS to h1, and have approved i797A with I-94 and working with my current employer.

Got an offer from another company, and they filed my H1b transfer, and got the i-797A approval with I-94.

So my question here is, can I join the new company using the H1b transfer approval, even though I don’t have H1b stamp at all in my passport? Will this be a valid H1b transfer?, or should I go back to India to get my H1b stamping to join the new employer?

After H-1B transfer is approved with the new employer, how long do I have to decide if I can to join the new employer? Can I join after 90 days of H-1B transfer approval? Is there a deadline?

My employer ended my employment due to COVID reasons on May 31, 2020 but I never received an official termination letter. Calculating the grace period depending on the assumed termination date mentioned above, I have till July 30 to find a new job. Should my new employer give me an offer or start the H1B transfer application before July 30? What happens if they fail to do so in time? Can I extend the grace period on the basis of having an offer in hand or maybe because of the pandemic? My final interviews with potential employers are being withdrawn because of the time restriction.