Learn Dutch: Mogen we hier parkeren? - Are we allowed to park here?

You would add niet right after the place (hier), making the sentence: Mogen we hier niet parkeren? In Dutch, niet generally comes after the time or place, but before the main action verb at the very end of the sentence.

Why is parkeren at the very end of the sentence?

Because of the verb mogen (to be allowed to). Mogen is a helper verb. When you use a helper verb in Dutch, the main action verb (like parkeren) stays in its full dictionary form (the infinitive) and gets pushed all the way to the end of the sentence.

Why does the sentence start with mogen instead of we?

Because it is a yes/no question. Just like in English, to turn a statement like we mogen (we may) into a question, you swap the subject and the verb: mogen we? (may we?).

Can I use kunnen (can) instead of mogen (may) to ask this?

In English, people often ask "Can we park here?" when they mean "Are we allowed to?". In Dutch, you should stick to mogen for permission. If you ask Kunnen we hier parkeren?, a literal-minded Dutch person might point out that you physically can fit your car there, but that doesn't mean it is legal!