Translation:I swim every month.
The audio sounds like she's saying "ma-i-tsu-ki" at the beginning. Is this the correct pronounciation?
がつ, げつ, and つき are all readings of 月. When you see kanji combos (jukugo) like this, they typically use the on'yomi reading, which in this case is つき.
That is not quite correct. つき is kunyomi, がつ and げつ are on'yomi, more specifically, がつ is 慣用音 (kan'yōon) and げつ is 漢音 (kan'on).
There is combo kanji that uses kun-kun reading if I'm not wrong that is one of those
It's not, but being picky about grammar, I'd suggest a comma after month. Report it.
To "go swimming" is a progressive actiom and the sentence as written does not allow for that translation.
No, "go swimming" is not a progressive action, as it would indicate a habit in the above sentence.
No, if you use およぎています, it's more like running. わたしはおよぎいます is "I am swimming" (present tense), so it doesn't make sense when describing a habit or something you do every month.
"I am swimming every month." Nope.
a) For reference, the progressive form of およぎます would be およいでいます, not およぎています.
b) As clickonwhatnow said, "I go swimming" is not a progressive form. I think the closest translation for that would actually be およぎに行きます, if we want to be precise about it.
That is not correct at all. This is simple present with a gerund after the primary verb. It should be reported as a correct answer.
It doesn't sound quite right in English. It works for daily, not so much for monthly.