Employers do not seem to be openminded at all. It's like you take it or leave it. To them it seems that internet is the solution.

I have had the same problems as you. I suppose that's because by advertising on the internet, employers can usually attract many more jobseekers than they ever could before. Unfortunately for us, they are spoiled for choice these days, additionally due to the downturn in most Western economies a factor that has also increased job applications for EFL work in China as well as elsewhere. So, potential employers can afford to be inflexible re the terms and conditions of their teaching contracts. It's now a case of 'take it or leave it' as regards the contract on offer. If you won't take it, they will offer it to another jobseeker, and so on, until somebody accepts their initial offer.

Also, I seem to have noticed that worries if I speak Chinese as it may not be an advantage for the job for some reasons. Well, I do not use my poor Chinese in classrooms, but I do observe the office talks more and more often. :)

If you speak good Chinese, you can pick up what's being said in the office. That would mean they'd have to watch what they're saying in Chinese in front of you, or else you'd pick up things said about you or your fellow foreign teachers, or even other stuff they didn't want you to overhear!