Learn Polish: Pracowała na zewnątrz rezydencji, którą kupiłeś. - She worked outside the mansion which you bought.

The phrase na zewnątrz (outside) is a compound spatial preposition that always requires the Genitive case. Because rezydencja (mansion) is a feminine noun ending in -cja, its Genitive form takes the -cji ending.

Can na zewnątrz be used on its own without specifying the location?

Yes, it can. Just like in English, you can drop the location and simply say Pracowała na zewnątrz (She was working outside) to act as an adverb of place. You only need the Genitive noun when you want to specify what she was outside of.

Why is the relative pronoun którą in the Accusative case when it refers to rezydencji, which is Genitive?

A relative pronoun matches its noun in gender and number (both are feminine singular here), but its case depends strictly on its grammatical job in its own clause. In the second half of the sentence, the mansion is the direct object of the verb kupiłeś (you bought), which requires the Accusative case: którą.

Why do the two verbs in this sentence use different aspects?

Pracowała is imperfective because it describes an ongoing, continuous background action in the past (she was working). On the other hand, kupiłeś is perfective because buying the mansion was a single, finalized event.