1) you can have a try to apply for visa in Singapore with the flight ticket from Kuala Lumpur to hainan, generally speaking, the visa officer will pay attention to return flight rather than your flight ticket to China because the return flight ticket can prove that your departure from China, you hold Singapore work permit, you are allowed to apply for visa in Singapore
2) you can apply for multiple entry visa, the worst thing is that you get a single entry one, you'd better provide the certificate to prove that you need multiple entries, such as copy of your Chinese visa in the past years, transportation plan, you need go to mainland China, hong kong, mainland China, then the visa officer will know that you need double entries or multiple entries
3) the visa fee is listed on this webpage, it takes 4 working days at Chinese embassy in Singapore, at least 3 working days if you aaply for express service.