I was in similar situation in 2011.
i) Its takes 2-3 weeks to get receipt and 2-3 months for approval
Before F2 is approved:
ii) On the day of layoff, without any second thought file F2 using COS form I539.
a. If during the F2 processing you get a job, ask them to file H1b in PP. Once H1b is approved (and F2 is not approved), you would send the H1b approval with F2 receipt to USCIS with an application to cancel COS to F2 stating you already have got legit visa status. They will cancel COS to F2 processing and sent you receipt. Call to USCIS to get the address.
b. Because your F2 is not approved, it would be considered as H1b extension (transfer iow). You should be eligible to work on receipt.
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a. Yes, you can go for another masters. No OPT allowed this time. You can do only one OPT for same level of education.
b. You don't need to leave USA. If F2 processing is still going on you need to use H1b to F2 COS receipt to file F1 COS. This receipt along with your last H1b pay-stubs shows your legal status in US while filing COS to F1.
c. You don't need stamping if staying in USA. Visa stamping is needed only to enter in USA (for Indian nationals).
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After F2 approval:
a. Employer will file cap exempted H1b for you with COS F2 to H1b.
b. You would be eligible to work only after approval not on receipt. Ask them to file H1b in PP. Earlier approval, earlier eligibility to work.
c. No need to leave US, again, Visa is needed to enter in US. As long as you are getting new I94s with approvals, you are good.
If you maintain and proof your current legal status, you can cos to F1, no need to leave USA.