Learn Russian: Чтобы синхронизировать файлы офлайн, нужна подписка. - To synchronize files offline, a subscription is needed.

In Russian, подписка (subscription) is the grammatical subject of the main clause, not the object. The literal translation is "a subscription is necessary." Because подписка is a feminine noun in the nominative case, the short-form adjective нужна must agree with it in gender.

Is the verb синхронизировать perfective or imperfective here?

It can actually be both! Синхронизировать is a biaspectual verb, meaning the exact same form serves as both the perfective and imperfective aspect. In this context, it functions as a perfective verb because the sentence focuses on the completed result of syncing the files.

Does the borrowed word офлайн change its ending depending on its role in the sentence?

No, офлайн is an indeclinable borrowed word. It never changes its form, regardless of the case or its grammatical role. Here it acts as an adverb modifying the verb синхронизировать, but even when used as an adjective, it stays exactly the same.

Why do we use чтобы followed by an infinitive here instead of a past tense verb?

We use чтобы with the infinitive синхронизировать to express purpose, meaning "in order to." You use the infinitive rather than a past tense verb because the implied subject doing the syncing is the same unstated person who needs the subscription.