How can i renew my working visa? if not, what kind of entry permit should i apply?

I have a working type for the past year in China, which will expire on Feb 25, 2015.

However, i have recently left the company and am doing freelance work until my next employement. Can you advise what kind should i apply for? is it F or L type with multiple entries?

Can i do the entry permit in Singapore as i will be returning for the CNY holiday soon.

Last question : do i need a Residence Permit for the application?

Your advice is much appreciated.