if your new child is registered in your embassy, this child is a citizen of your country and not Chinese, therefore you can have another one - recommend registering your child as a  citizen of your country if born in China!

1. Would the child be allowed to attend school in china?

yes but but you better think long and hard about this (either way you will have to pay. my advice for the sake of your child, if you can't afford an intl school do not move to china. or at least have your child go to school abroad.

2. Does the law treats the child same as the children born to a Chinese national?

your child is a foreigner. and will be reminded of that every single day in school by teachers , staff and students. (because if you are not chinese sth is wrong with you)

3. Can we have another child later in life?

yes

4. What other legal issues should we be worried about if any?

the other posters will cover this

Crimochina shut up!

I'll tell you how it is.

My son is from a different marriage, he's been going to schools out here for years, in a government school. Because I have a legal working visa. If you work for a legal school your child can go to a chinese school.

These schools are fine. Don't worry too much like others who just enjoy being pessimistic.

Here are the requirements for Shenzhen, but it will be the same in other parts of China.:

Third, the children of expatriates

1, the student must apply for schools in the "school of foreign students enrolled in Shenzhen Application Form" (available in Shenzhen City Department of Education Web http://www.szeb.edu.cn/ homepage "Basic Education two" in the "Download Forms "column downloading) on" their schools opinions "sign an opinion column, and official seal.

Two, primary and secondary school students to apply for admission to the district administrative department of education shall be in the "school of foreign students enrolled in Shenzhen Application Form" on the "District School Board Opinion" column sign an opinion, and official seal.

3, the school "Admission Notice" or the letters indicate the duration of study.

4, students and parents, or a copy of a valid passport and visa valid identification guardianship trustee copies (original inspection, archive copies).

5, kinship certificate (subject to our embassies certification) (original inspection, archive copies).

6, the parent or guardian in the deep work units responsible trustee of the original proof.

7, the trustee responsible parent or guardian in the deep work unit business license or organization code (the original inspection, archive copies).

8, if the applicant parents are not residents of Shenzhen (visa type "F", "L", purpose of residence is not "employment" or "office"), commissioned by their parents or foreigners resident in Shenzhen, the Chinese people to fulfill the duty of guardianship the certificate shall be subject to the domestic commissioned notary public or our embassies notarization, authentication, both by the client must provide a valid passport or identity card and residence permit (non Shenzhen accounts are required to provide a residence permit), proof of work units in the deep , work unit business license or organization code (the original inspection, archive copies).

9, students, parents or guardianship trustee "Temporary Accommodation Registration Form" (original inspection, archive copies).

10, in Shenzhen, valid proof of purchase or rental (original inspection, archive copies).

11, after receiving the school, the District Education Bureau Education Division of First Instance of foreign students by the school hand submitted Shenzhen Bureau of Basic Education two approvals (original inspection, archive copies).