tax on CPT(F1 VISA) if stayed on L2 for 5 years


My wife was on L2 VISA for above 4.5 years and now moved to F1 for last 3 months. and I moved to L1B to H1B VISA. She is going to work on CPT very soon.

I have following queries.

  1. My wife is in US on F1 VISA for last 3 months only, is she eligible to get tax exemption from FICA(social security and medicare) if she works on CPT (even she has now spent more than 5 years in US on L2 status)?

  2. How should I file my tax return ? Married filing Jointly or Married filing Separately ?