Are experiences in teaching TOEFL important?
Definitely. A person can score a perfect score in TOEFL while that person can be a horrible teacher. A person can be an excellent teacher even if he didn't score well in the test. It takes time and experiences for a person to study deeply into the test, to discover the techniques in answering questions to better help students.
Are all Asians good at math?
Not all of them but most of them are. And I am one of those that are good at math.
Does speaking mandarin fluently mean being able to be a good teacher in teaching the language?
Certainly not. It seems easy for a mandarin-speaking person to teacher others the language. However, that person has to be fluent in both mandarin and english. Furthermore, when it gets to grammar in a language, certain knowledge and skills are required to explain explicitly.