You can change to H1B status in U.S. Just ask your employer to apply it for you. But keep in mind, there is no quota for H1B now unless you work for instituions which require no H1b quota.
EAD can be obtained after you file I-485. If you born in mainland China, you can't apply I-485 due to the retrogression. You have to wait.
After you get H1B, if you leave U.S, you need to apply H1B visa in American Embassy to come back.
