Fingerprinting (I485) and H1-B

I have just submitted my I-485. I am wondering when I can go to take the fingerprinting. Because I am trying to change job in another state, I want to finish the fingerprinting as soon as possible.

By the way, I am currently holding H1-B in a university. Can I still get H1-B in a new university? If I can, how to do it? How long time will it takes? If I submitted the H1-B application, can I go to work while the new H1-B pending?