What are my options for applying for permanent residency?

Considering you are on P1 status, you might be eligible to EB1 Status which would allow you to get a green card. However, that is not the only...

H1b visa. If my employer files an I-140 petition, can my wife on H4 also be included in the adjustment of status for green card.

Yes, she certainly can. She will be subject to separate filing fees.

Yes, you certainly can apply for the H1B under the Master's Cap. I would certainly advise you to try for this year's lottery before exploring any...

How can i switch from H1B to L1A in order to get my green card filed in EB1C category?

This is a very detailed oriented category, to sum it up, it doesn't really matter if you are currently on H1B or L1A to be eligible for EB1C...

My wife wants me to stay in America with her, she came to visit me earlier this year now i am here in America with her i entered

There are two main factors that go into play in terms of you breaking any law as your asked. Is your wife a U.S. Citizen or a Permanent Resident?...