Greetings Saloonies,
First question is, if my gf and I are hired as a couple will we get an apartment together? The reason I ask this is because I read that it is illegal for couples to live together unmarried in China? Is there an exception to that rule for foreigners? Second question is, would it be too late for us to land a job at a uni or private school now? I read that it is all about timing, as many of the FAOs have their inbox's flooded and tend to be overwhelmed but is there a cut off date?
I am truly looking forward to this relocation and sharing my adventure!!
~Cheers 
I can let you know what i think the probable answer to your questions are;
1. Tbh, I don't know the answer, but why not try to get 2 apartments. If you're both working for the Uni they're not going to be worried about you stopping over in each other's places. I'd use one apartment for work and the other for, er, pleasure. There's no actual exceptions to laws for foreigners, but as you can probably appreciate, China being such a huge country is heavily dependent on buraucracy and local intepretations of laws.
2. Although I'm sure there are some Uni jobs going, I think you'll find that most Unis are on holiday, and therefore there's nobody at work at those Unis finding teachers. Some Unis will be open and / or looking for teachers, but not many, as it is very late in the day. I'm afraid most people apply in March / Apriil, and the Unis sort out their teachers in April / May. Loads of exceptions to the rule of course. Lots of folk on this forum got their jobs in June, and even this month, July, but I believe that most of them had started their hunts for jobs quite a while before.
To be honest, if someone offered you a job now they would be cutting it a little close to get all the paperwork done in 5 or 6 weeks. It's possible of course, but they're on holiday. Teachers already in China, and ideally in the city, have a huge advantage. People with experience have an even bigger advantage. Also, you need to find somewhere with 2 jobs. I believe that with a huge amount of work and a bit of luck over the next week you could possibly get a Uni job somewhere. Send all your info (passport, copies of quals, photos) to every University and Private school that you can find in China and hope for the best since with so little time to vet Unis and schools you would be taking a huge gamble. If you get 2 jobs in Jing'an at this point you will have transcended luck and become the chosen ones that no force of fate can oppose.
On the whole, I think it is probably much better to get some teaching experience over the next month or two of summer and apply for jobs starting the following term, (roughly end of February). There's less jobs and I'm not sure when you should apply; probably nov or December.
The other alternative is to get work at a 'language mill' for a year. They'll practically gobble you up, and if you can start by the end of August, your sentence, sorry i mean contract, with them will be up nicely in time for next September.
The other option (good or bad) is i suppose recruiters, as they will know which Unis and schools are lookinhg for teachers. Sorry to be so negative. I hope that other posters can give an opposing and more optimistic response.