How often does a teenager need to have psychotherapy in order to see benefits?

Weekly or more. Most psychotherapy for teens or adults works best when done on a regular, planned schedule of at least one session weekly. More intensive therapy, esp. Of the psychodynamic type, may occur two or even three times a week. The reasons for advising such frequent therapy are complex, and not necessarily related to severity. Therapy less than weekly can still potentially help, but less reliably.
Depends. It depends how chronic and severe are the sypmtoms.
Well, it depends... Teens can have as many troubles as there are types of therapies. That is, an endless amount. So, the answer depends on what the question is...Meaning, what are we trying to "fix?" some problems respond quickly, within weeks, to structured therapy such as cognitive-behavioral (cbt), other problems require years. Therapy tends to work better than drugs in the long term. It's worth it.