Learn Polish: On wciąż mieszka w Krakowie.

In this sentence, wciąż translates to "still" and emphasizes that a situation is ongoing. You could easily replace it with nadal (still) with no change in meaning. You might also know jeszcze for "still" or "yet," but wciąż and nadal are usually preferred when you want to highlight a continuous, uninterrupted state, like living in a city.

Why does Kraków change to Krakowie, and where did the ó go?

The preposition w (in) requires the Locative case here. For masculine nouns ending in a consonant like -w, the Locative ending is -ie. Adding this ending softens the final consonant into -wie. Additionally, the letter ó in Polish frequently changes back to an o when you add endings to a word (as the syllable is no longer closed). So, Kraków becomes Krakowie.

Is it mandatory to use the pronoun on here?

No, you can drop it! The verb ending in mieszka already tells us the subject is third-person singular (he/she/it). If you've already been talking about a specific man, you can just say Wciąż mieszka w Krakowie. Using on here adds a bit of emphasis or helps clarify exactly who you are talking about if the context isn't obvious yet.

Can I change the word order and put at the end of the sentence?