H1B Revoked - Cap Exempt?


April 2018 – Lottery picked
November 2018 – USCIS Site visit
December 2018 – Went to India, got H1B Stamped, came back
Feb 2019 – Intent to Revoke Notice was issued. According to them, the job description we submitted doesn’t match with the job description of approved LCA. LCA was approved for Cost-Estimator but USCIS claims the filed job description aligns more with Construction Manager than with Cost Estimator. Were asked to file a response with sample of work.
March 2019 – Attorney filed a response with required documentation.
June 2019 – H1B Revoked, so I am out of status – they found proofs unsatisfactory. Asked to file an appeal within 33 days.

My questions:
Can my company refile H1B instead of appealing it?
I have an approved visa stamp, how long can I stay in US?
Can I apply for jobs, go for interviews and if I get hired can I get the new company to file a new H1 petition?
If we end up appealing it, what all should we include?
What must one do in this situation?

Well, if it is revoked, not sure, if you would considered in cap to refile. You need to check with your attorney. Your approval stamp does not mean anything, if you do not have H1B Status. Read US Visa vs Status. Appealing is probably the thing to do, check with your attorney and plan it accordingly.