Green Card for medical lab technologist

[vet2000]

I am working medical lab technologist.at state hospital of newyork and getting paid by newyork state.I want to apply for green card now.Am i eligible to apply for EB2 category.I have BS degree with one year of experience with same hospital.What is current processing time for I-140 and 1-485 for EB3 for Pakistan National cadidates.
Will the green card process be fast if working in State hospital?

thanks