can I put "xin" in the sentence?
Technically yes but "xin làm ơn" really means you are on your knees begging someone to do something. Either "xin nói tiếng Việt" or "làm ơn nói tiếng Việt" would be equivalent to "please".
Lam on Anh noi tieng Viet is also a correct translation since its specifically referring to the male figure youre speaking to
"Xin vui lòng nói tiếng Việt" should also be correct.