Laid off on H1b, transfer questions

I was laid off on 6/4 so my 60 day grace period ends on 8/2. I am on my 5th year of H1b, have approved I-140 and am waiting for my priority date of April 2018 to become current. I’ve compiled a number questions, really appreciate any insight!

  1. If I find a new employer to sponsor me and file the transfer, but I don’t receive the receipt notice within 60 days, do I need to exit out of the US on 8/2 the latest and come back once I receive it in mail and obtain new visa stamp (current visa expired)?
  2. With the above scenario, if I have applied for B2 visa during the 60 days on the possibility of not finding a job and needing additional time to wrap up affairs and leave the US, but then receive the receipt notice past the 60 days while I was in the US, can I start working right away? How does it compare if B2 COS was pending vs. approved?
  3. If my B2 COS is approved, what document will I receive and how do I obtain new visa stamps? How do I know how long the visa will be valid for? I know that they were giving out 10 year multi visit ones.
  4. My current I-797A from previous employer will expire in August 2021, after my new employer files petition for H1b transfer, will I receive a new receipt notice showing the same expiration date? Do I receive another 3 years’ extension after?
  5. How long does regular and premium processing usually take for me to receive the receipt notice?
  6. How common is it that a firm would sponsor your H1b visa but NOT sponsor for your green card?