1)Yes,2)Yes,3)Depends.

You are on H1B status now, not H1B visa. If you were rejected for visa in Canada or Mexico, then you need to go back to China for visa. It depends on your company or boss once your H1B visa got rejected. If they are willing to wait until you get back (supposed you got rejected or security background check), you don't have a status problem. If they are not willing to wait, then you will have a status problem.