I have broken 2nd and 3rd metacarpal. How long is the recovery after treatment with plates and screws?

Depends. We really have to see the x-ray to see if it is a stable fixation to begin early movement which will return you to normal activities sooner. Ballpark woud be 6-12 wks.
8-12 weeks. You have to keep in mind that every thing went right with surgery, no complications.