Yes, but only if they’ve applied for and received a work permit (EAD).

Without the EAD, they must wait until permanent residence is approved.

Some people keep working on an existing visa status if it’s still valid while their green card is pending.

Yes if they applied for a work permit (EAD) along with their green card, they can work once the EAD is approved.

Yes, you can work once you get your work permit while your marriage green card is being processed.