Syyskuu on hyvä kuukausi aloittaa uusi harrastus, kun arki on taas alkanut.

Here uusi harrastus is the object of aloittaa. The action is seen as a complete whole, so Finnish uses a total object, not the partitive. In this kind of infinitive construction, where no explicit doer is stated, that total object often appears in the nominative singular, which is why you get uusi harrastus.

A useful comparison is:

• Haluan aloittaa uuden harrastuksen = I want to start a new hobby
• Syyskuu on hyvä kuukausi aloittaa uusi harrastus = September is a good month to start a new hobby

So the case changes because the structure changes.

Here kun is best understood as when or once. It gives the time/background for the main statement: September is a good month for this when everyday life has started again.

Finnish kun can sometimes also feel a bit like since/as, depending on context, but in this sentence the time sense is the most natural one.

Koska is more clearly because, so it sounds more directly causal. Kun is often preferred when the idea is about timing or background circumstances.

So:

• kun arki on taas alkanut = when everyday life has started again
• koska arki on taas alkanut = because everyday life has started again

Both can make sense, but kun sounds more natural here.

Arki means everyday life, daily routine, or ordinary weekday life. It often refers to the normal pattern of work, school, commuting, schedules, and responsibilities, especially after a holiday period.

So in this sentence, arki on taas alkanut suggests that the relaxed holiday season is over and regular life has resumed.

On alkanut is the present perfect and means has started. It describes something that began before now and is relevant now.

Compare:

• arki alkaa = everyday life starts / is starting
• arki alkoi = everyday life started
• arki on alkanut = everyday life has started

The sentence uses on alkanut because the routine has already begun, and that current situation is what makes September a good time to start a hobby.

Because kun arki on taas alkanut is a subordinate clause. In Finnish, subordinate clauses are normally separated from the main clause with a comma.

So the comma is standard punctuation here.

Yes. Finnish word order is fairly flexible, and changing it can shift the emphasis. For example:

• Kun arki on taas alkanut, syyskuu on hyvä kuukausi aloittaa uusi harrastus.

This version puts the background situation first. The original begins with Syyskuu, so it presents September as the main topic right away.