H1 Transfer and GC dates

[mikehill]

Hi,
Currently, I am on H1B for company A. My GC filing is under EB3 and my priority date is December 2013. I am planning to consider a full-time offer from company B and I have few questions on this matter.

1. Does my priority date still be valid once I transfer my H1B to company B
2. Is there a chance that my current employer withdraw my GC right after I move to company B ? Would I lose my priority date in this case ?
3. Since my current GC filing is under EB3 category, can I still carry the same priority date if company B files my GC under EB2 ?

Any help in this matter is really appreciated.

Thanks