1. My wife's Tier 2 ICT Long Term Staff Partner VISA expires in May 2016; I need to extend her visa. Which application I need to use SET(O) or SET(M) or FLR (M)
None of the forms you list. Set(M) and Set(O) are for ILR, she doesn't qualify yet for ILR. If you apply FLR(M) it will reset her clock to zero and she will have to wait another 5 years on FLR(M) - 2 x 2.5 year visas - before she can apply for ILR. She should extend her visa as a Tier 2 ICT dependent which is an online form process, see PBS Dependent Partner Online (click) and also Tier 2 ICT dependent (click). The immigration health surcharge is NOT payable for Tier 2 ICT dependent.
2. When is best time to apply for my wife's visa extension. Now or in May 2016?
No sooner than 28 days before her current visa expires.
3. Which is the earliest way of getting ILR/Citizenship for my wife? though my visa status or through my kid's dependent as he has British passport. I will be eligible for British Citizenship in May 2016 and will get British Passport by OCT 2016.
The quickest way is if she continues on Tier 2 ICT dependent.
4. If I have to apply FLR(M); do I need to select "First period of leave to remain" or "Second period of leave to remain"
See #1 above, this route will reset her clock for ILR. She will lose the time she has already spent in the UK as this cannot be added to the NEW 5 year period IF she applies on FLR(M)
5. If the Visa is issued based on FLR (M) then what will be the visa period (2 years or 3 years)
2 x 2.5 year visas
6. My wife has completed post graduation in English medium. Please let me know whether this will be sufficient or need to take any English Language
Is it a degree recognised on the PBS calculator? IF you apply FLR(M), she needs to meet English level A1