Learn Polish: Dopóki jestem właścicielem, nie wolno tu hałasować. - As long as I am the owner, you must not make noise here.

In this sentence, it means "as long as". Dopóki translates to "as long as" when it is followed by an imperfective verb describing an ongoing state, like jestem (I am). If you wanted to say "until", you would typically use dopóki nie followed by a perfective verb.

Why is the word for owner, właścicielem, not in its dictionary form właściciel?

It is in the Instrumental case. You need this case because of the verb być (to be). Whenever you use a form of być to state what a person or thing is (like a role, profession, or relationship), the noun that follows must take the Instrumental ending.

Who is the subject of the second half of the sentence, nie wolno tu hałasować?

There is no specific subject! Nie wolno is a fixed impersonal expression meaning "it is not allowed" or "one must not". To state a general rule, you simply follow it with an infinitive verb like hałasować (to make noise).

Why does nie wolno take the imperfective verb hałasować instead of a perfective equivalent?

When nie wolno is used to express a general, absolute ban (meaning "you must never do this under any circumstances"), it pairs with an imperfective verb. This emphasizes that the activity itself is completely forbidden at all times.