2. if hu*****and's employer can sponsor the greencard application, then he first need ask them to apply for LC, since most postdoc and their employer didn't sponsor the greencard, they need to apply via NIW, EB1 etc, which didn't require employer's sponsorship, but require the applicant have very strong background.
3. once your hu*****and start to apply, he can also apply for you.
4. once you have GC, no F-1 needed, but before they approve it, you need to stay with your F-1 visa