You have stayed inside US on H-1 (I assume H-1 was approved w/ COS) for almost 6 months now. This is a SERIOUS ISSUE.
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Another employer can file cap-exempt petition (aka H-1 transfer) for you. However, most likely it would be approved w/ consular processing as you are not maintaining legal H-1 status.
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If you want to move to H-4, then you should leave US and return on stamped H-4 visa. You cannot apply COS from inside US as you are not maintaining legal status.
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A can revoke their H-1 petition anytime they want. However, you would still be able to get cap-exempt petition through another employer by submitting a copy of approval notice as reference.
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Yes, see (5)
By law, A is required to pay you the salary as per the LCA. Talk to them about it, and complain to DOL if they don’t oblige. But start getting paid ASAP.