Learn Polish: Nie wolno tu spać! - Sleeping here is not allowed!

The word wolno means "it is allowed" or "one is permitted." It is an impersonal expression, meaning it doesn't need a specific person attached to it. When combined with nie, it simply means "it is not allowed" for anyone in general.

Does wolno mean "slowly"? I thought I learned that word already.

Yes, you probably did! Wolno is a tricky word because it has two completely different meanings depending on the context. It can mean "slowly", but when used before a verb to describe rules or permissions, it means "allowed".

Why is the verb spać in its basic dictionary form?

After wolno or nie wolno, you always use the infinitive, which is the basic, unconjugated dictionary form of a verb. So, nie wolno spać translates literally as "not allowed to sleep".

Could I use tutaj instead of tu?

Yes! Tu and tutaj both mean "here" and are completely interchangeable. Tu is just a shorter, very common option for everyday speech.