"My aunt often writes letters."
Translation:Min faster skriver ofta brev.
tant is technically correct but old-fashioned bordering archaic. It shouldn't be used or taught in any kind of modern Swedish.
Have a look here :https://ne.ord.se/ordbok/svenska/engelska/s%C3%B6k/tant
Since we can't know if it's the mother's sister (moster) or the father's sister (faster), I too think tant should be accepted, even if it's not as precise as moster/faster
The adverb is usually in the third position in a sentence in swedish. It would change if the adverb was part of a subordinate clause : it would then be placed before the verb.