Application and renewal procedure for the S1 visa and also travelling

I came to China for studies, and have 2 years to go. I'm planning to invite my spouse and son to live with me the rest of time. Do I need some kind of approval from my school or letter so they can be dependent on my X type or they'll get visa when I'm applying to renew it?
We have different nationalities in matters of passport, will this cause problem?

Also S2 holders must stay in China during the period on the paper."
Does this mean that we cannot travel together even for a short holiday?

Thank you in advance.