My ARC is valid only for another 4 months

Hello,
I am from Mexico and I've been living in Korea for 3 months. I want to go on a trip to China in December and visit various cities. I need a multi-entry visa but my Alien Card is valid only until 2016.03.31 so I guess it will be denied if I try to apply for it now. What can I do?

Could it be issued in Hong Kong?
Is there absolutely no possibility of me getting the entry permit if I apply for it now?
I also want to know if the fee I have to pay is that of "other countries"

Thanks a lot!
regards,

Janette Rubio
Mexico