Shanghai PVG - 24 hours connection - where to sleep?

Thank you for your previous answer!
Another question re having a 24 hours connection at Shanghai PVG -
I have tried to book hotel within terminal 2 but there are no more rooms.
1) is there another hotel in the airport?
2) is it allowed to sleep in a hotel near the airport but outside the terminal
if yes -
1) what happens with my luggage
2) will I have trouble going back through immigration?
3) is it something that I need to coordinate in advance in terms of immigration/visa - if yes- who do I contact?
Thank you so much
Reut