1. My son has ">LPR status and wishes to marry a girl who is on student visa valid for next 3 years. Is she required to maintain her F1 status after her petition is filed after marriage.? Can he apply forAOS after filing the petition? Appreciate your guidance.

2.Can she stay as long as she has valid F1 visa and ">opt to follow? After this period sBhe may try for H1

1. She cannot apply for her AOS unless the priority date is current (which takes several years). And she has no legal status just because an I-130 was filed or approved. An additional problem is when an F-1 marries a green card holder, govt. can take that to be a violation of their non-immigrant intent, if that becomes an issue. That problem should not exist as and when she takes on an H-1.
 
2. I see no law against staying and OPT, but marrying an LPR can be problematic as indicative of immigrant intent. H-1 is the only safe option.