回複：持大學的H1B可以在公司工作嗎？

too many questions. Cap of H-1B for those with graduate degree in U.S. has not been reached. If you have H-1B at University and you wanna work at company, you have to apply another H-1 sponsored by company. Better not to change to J-1. You need to file waiver for immigration purpose (I-485) or H-1.