Can I apply for a student visa in Kazakhstan?

Peris, if have valid resident permit for employment there, I think you are able to apply from Chinese embassy in Kazakhstan. Please ensure that your resident permit should be valid at least six months.

Do you only take the exams or need to study for a while in PRC before you take the exams? If you just take the exams, I think a L type is enough. If you want to study and then take the exams, then you should apply for X type. It requires the admission letter from the school. If you plan to apply for X1, JW202 form is also required.