Each of you have the option and can exercise it when you want

Yes, H-1B petition can be filed by employer with pending waiver application

Entering the U.S. on visitor visa with intent to stay and apply for residency is considered preconceived intent and has serious consequences. ...

COS application is abandoned upon departure

You can always seek to withdraw, however attention to it from USCIS can be sporadic or uncertain.

Usually we do not recommend filing COS as dates are blurred. But you may maintain H-4 so you do not use up H-1B time.

Most immigration attorneys here can help. Reach out directly.

IO will seek the purpose of entry and depending on the reason, admission is possible

F-1 is to study not to be abused to stay and work. Other options can be discussed with consulting attorney.

Post your question or reach out to an attorney through "Find a lawyer" here