That's because 'w wrześniu (sic)' ('in September') would be too awkward to pronounce, so we say 'we wrześniu' instead.
In general, we use 'we' before words starting with either 'w' or 'f' followed by another consonant. Other than that, we use 'we' in front of the pronoun 'mnie' ('we mnie' - inside me) and few other words (e.g. 'we śnie' - 'in a dream').
Not really, not in Polish. Generally "I go" is translated as "chodzę" and "I am going" is translated as "idę".
"We wrześniu idę do szkoły" would generally mean that I'm starting school in September. "We wrześniu chodzę do szkoły" is not the greatest sentence ever, but it means that I spend all my weekdays in September in school.
The sentences about school kinda mess up with the chodzić/iść distinction. I guess this can be 'idę' in this particular example, as this may be easily understood as "I will start the school year in September" (because it's September, and Poland).
But generally, the distinction you wrote is wrong. We differentiate it this way:
to go, to walk (generally, habitually) = chodzić
to be going, to be walking (right now) = iść
to be walking (but without a purpose/direction, just walking around) = chodzić
This of course only applies for going on foot.
I have a question because I am not an english native speaker. Duolingo focuses on the distinction between chodzić and iść as equivalent to that between simple present and present progressive. But as far as I know present progressive is not as present as it seems. Is it not right to say f.e. "I am going to Spain in July" or "Next year I am going (regularly) to the gym."? Is therefore translating the given sentence as "I am going to school... " (instead of the better "I am going to go to... " of course) really that incorrect?
Sorry to repeat that old topic again.
"I am going to Spain in July" is so-called "Present Continuous (Progressive) in the future meaning", and that's a normal usage of this tense. Polish uses it the same way, it doesn't necessarily have to mean "I am going to Spain at this precise moment".
However, "I am going to go to" is a different thing, "I am going to" here means "I will" and expresses Future Tense. Or potentially "I am planning to".
This particular sentence no, because it uses "chodzę", which calls for Present Simple. The sentence basically says "I spend a big portion of September in school", "September is a month in which I go to school, there's no holidays".
I guess especially given that it's September and not any other month, one would rather expect "idę do szkoły" = "I'm going to school" = "I'm starting school"...