I am from UK, born in INDIA, naturalized as British.

I have a 4 yr degree from INDIA (BSC Agriculture Sci. Edu. Eval. Done) and 12 yrs of IT experience (11 in UK). A company is ready to sponsor my EB2 & H1b. These job roles do not require an IT degree, any degree with 5 yrs experience is fine.

1) Am I eligible for EB2? Main concern is, my degree is not related to my current work or proposed EB2/H1b jobs, though jobs do not require an IT graduate.

2) EB2 application.
a) Is it possible to apply for EB2 without me coming to US on H1b?
b) Is it better to apply for EB2 once I am on H1b in US?
c) Assuming I applied for EB2 before coming to US on H1b, Does it impact on my H1b processing?

Your advice on each situation above and risks involved is greatly appreciated.