Moving to Shanghai and Job Hunting?

Hello, i have few question and hope you can help me.
My fiancee received an offer in Shanghai and we are moving by the beginning of February 2017.
I am coming with him on a Tourist visa with the validity of 30 days. i will be looking for a house and do other stuff that we need on relocation.
I have a concern with regards to my visa which is only 30 days valid.
Can i apply for a job while i am in China or is there any chance i can be employ?
Also we are looking to have an apartment in French Concession area, how much is the apartment range for a 1 bedroom and what is the best option we can have.

Thank you and look forward for your comments.