(A) How should I respond to teacher in writing? Usually when addressing a teacher, "Mr.", "Mrs.", or "Ms." is sufficient. "Sir" or "madam" is too formal for teachers. Most instances when I hear "sir" or "madam" is when someone is trying to get the attention of a stranger or when a store clerk is addressing a customer (It seems to be a common practice in the USA, not where I live though.) Also, it's best to avoid abbreviated "madam" to "ma'am." For professors, you would just say "Professor" followed by their last name. (B) How should I respond to those worthy of respect besides teacher? Some professions have titles associated with them, but a lot of them do not. An example is "Dr." for addressing doctors.

If you are writing in a formal style, it might be strange to use that kind of phrase at all. "Yes" followed by a title seems more like something you would say in conversation, not in writing. Maybe you could give us some more context?

I would personally find out their surname, and use Mr, Mrs, or Ms. However, a lot of teachers these days are happy to be called by their first name. In schools, however, I have heard "Sir" used as a gender-neutral pronoun. So, in some schools a female teacher will be referred to as Sir. The same thing happens in Spain, where I live. Perhaps this is a new trend?

Sometimes writing "Dear Ma'am/Sir" is useful if you do not know who you are writing to - for example, a cover letter. Usually, the use of the words, whether written or verbal, are meant as a substitute for a name when we don't know the name. As previously suggested, I would recommend using "Dear Ms. So-and-so" and skip the formalities. That said, a short response to a request, such as in an email or text, could certainly be, "yes, Ma'am", and would show respect.

The really useful answer is this. Each school has its own tradition, convention and subculture. So there is no general rule. At St. Martin's in London or the Parsons in New York, both artsy, everyone in on first name terms. At Cheltenham Ladies College, a traditional British high school for middle and upper class girls, it's always "Mrs. Robinson". At the police academy, it will be something else. Best advice: follow the usual practice of that institution.