1. Generally speaking, no, they don't.
2. Yes and no. It depends on the course.
3. Yes and no. It depends on what theories. Syntax, semantics, and phonetics are not theories.
4. It depends on a variety of factors. For example, if you're teaching, say, a TOEFL course, knowing something about the function and distribution of word classes would definitely come in handy when explaining why a given example is either correct or incorrect. If you're teaching kindergarten students, knowing something about developmental stages and how children learn language would definitely be a positive; e.g., spending a great deal of time on pronunciation isn't going to help them at that stage. If you're teaching junior and senior high school students, knowing that the 3rd person inflectional suffix -s (e.g., walks, eats, runs) takes time to filter its way in, would save you that time and effort you normally put in correcting the error.
There are many more examples ...
