They should have some registration with BC Corporate Registry not matter how the company is legally organized. The company will have a certificate issued by them, either as a native BC or foreign corporation. That is the one you need.
Not sure exactly what you mean. Whether you have to stay in the province once Permanent Residency is granted? I am not aware of any residency requirements once you become a PR, at least in BC. Just must remain until the entire PR application process has completed and you have landed.