Learn German: Passt bitte auf! - Please pay attention!

This sentence is a command directed at a group of people informally, like saying 'you all'. To make this type of command, you start with the normal ihr form of the verb (ihr passt) and simply drop the pronoun ihr.

What is auf doing at the end of the sentence?

The full verb here is aufpassen, which means 'to pay attention' or 'to watch out'. It is a separable verb. In a command, just like in a normal present tense sentence, the prefix auf detaches and moves to the very end.

How would I say this formally to someone I do not know well?

To give a formal command, you use the Sie form. Unlike the informal forms, you must keep the pronoun Sie in the sentence. The verb goes first in its infinitive form, making it Passen Sie bitte auf!

How would the sentence change if I were speaking to just one friend?

You would use the singular informal command. You start with the du conjugation (du passt) and remove both the word du and the -st ending. The sentence would become Pass bitte auf!