Learn Russian: Папа не идёт на рынок, он идёт в офис. - Dad is not going to the market, he is going to the office.

In Russian, в generally means going inside an enclosed space, like a building (в офис). на is used for open areas, events, and certain traditional public spaces. A market (рынок) is treated as an open space and historically takes на.

Are рынок and офис in the accusative case here? They look just like their dictionary forms!

Yes, they are in the accusative case because they are the destinations you are going to. However, for masculine inanimate nouns (objects and places, not people or animals), the accusative form is exactly the same as the dictionary form.

Why does the sentence use идёт for 'going'?

идёт comes from the verb идти, which specifically means going on foot in one direction right now. This tells us Dad is currently walking. If someone asked Куда он идёт? (Where is he walking to?), this is exactly how you would answer.

Could we use the word а (but/and) instead of just a comma after рынок?

Yes! Russian often uses just a comma to separate two contrasting clauses when fixing a misunderstanding (not X, just Y). But you could absolutely use а (meaning 'but rather') here: Папа не идёт на рынок, а идёт в офис.