Employer will provide introductory instruction and assistance with Chinese law and regulations. The Employer will also provide the Employer’s work regulations and the relevant foreign Expert regulations of the Chinese Government. Party A shall conduct direction, supervision and evaluation of Party B’s work. Party A shall provide Party B with necessary working and living conditions. Party A shall pay Party B’s salary regularly by the month.
Part B shall observe Party A’s working regulations and system concerning administration of foreign experts and shall accept Party A’s arrangement, direction, supervision and evaluation in regard to his/her work. Without Part A’s consent, Part B shall not render service elsewhere or hold concurrently and post unrelated work agreed on Part A.

Contract can be revised, canceled or terminated with mutual consent.

That's not everything, but I think a lot of the other stuff sounded pretty legit/okay. If something doesn't sound right, I will check to see if I left it out.

Point 1 - This is at odds with the official contract for public schools/universities. If the teaching is not up to scratch in the eyes of the employer, the errors should be pointed out, and the FT should be given a chance to improve. In other words, a written warning, then cancelled or out the door. A dismissal procedure is not in play.
Point 2 - I take it if you're fired for poor teaching, the 5.000 RMB fine doesn't apply.
Point 3 - I think what is meant is that you must teach according to the way the ChineseEnglish teacher wants you to teach. And you must let her train you.
Point 4 - Find out what they mean by this, 20 periods of teaching or 20 clock hours of teaching. The latter would mean you'll be busier teaching than the former would mean.
Point 5 - Five days per week, but is it Monday - Friday, or are Saturdays and Sundays included? And when does the teaching take place, I take it no evening work.
Point 6 - Is this 5 hours included in the office hors, or is it additional to them?
Point 7 - Why not 1/30 or 1/31 or 1/28 or 1/29 per day, depending on the number of actual days in the relevant month(s)?

Other points: First, is there a curfew at your accommodation, ie a gate locked every night at 11 pm, which would be restricting? Second, in a case of an unresolvable dispute, there is no option for you to get the SAFEA arbitration panel involved. this could include an accusation by you of unfair dismissal. Third, why no air fare allowance? Many employers offer at least 5,000 RMB for a 2-semester contract, and 2,500 RMB for a one-semester contract. Fourth, why no travel allowance, at least 1,000 RMB/semester? Fourth, I take it there aren't any paid holidays at Spring Festival or in the summer - in the case of a 2-semester contract, the major holiday in the middle should be paid. Fifth, how far is it from your abode to the classroom. If it isn't within walking distance, will they provide you with a bike? Sixth, how long is each 'teaching hour', for kindergarten students it'll just be 20 minutes. Sixth, what about medical insurance?

in a word, a typical training centre contract!