JedPewnego dnia, Ali-baba poszedł na spacer wdo lasieu.

If you're only talking about a single occurrence, it's better to say "pewnego dnia" otherwise it sounds a bit weird.. you could however say something like "Jednego dnia poszedł do lasu, drugiego do parku" since in that case you'd be enumerating things.

Ali-baba usłyszał głosy i szybko się schował się.

"Usłyszał głosy" makes it clear that this was a finite event. "Słyszał głosy" means that he was hearing voices continuously, and the phrasal verb "słyszeć głosy" often implies that someone is insane and that the voices are in their head so it could be misinterpreted easily.

Also the word order isn't exactly the same as in English, it can be a bit fluid but usually you wouldn't end any sentence with "się" unless it was followed by more information, for example "schował się w jaskini"

Nagle, pojawiła się grupa bandytów pojawiła się.