Marrying in China - Two different nationals

My girl friend and I are from two different countries. I am from India and she is from Bangladesh but she is studying in China. She has a valid Student X. I live and work in the US on a work Z. Can I marry her in China when I visit her later this year? Would I have any problem applying for her spouse visa for the US? Would our marriage in China considered legal in the US and in our home countries?