Learn German: Der Polizist hat in die Luft geschossen.

The preposition in is a two-way preposition. It takes the accusative case here because it describes the direction of the action (where the shot is going) rather than the location where the action takes place. If it were in der Luft, it would mean the policeman himself was floating up in the air while firing the gun!

Since a bullet is moving, why does geschossen use the helping verb hat instead of ist?

In German, we use sein (like ist) for verbs of motion only when the subject of the sentence changes their own physical location. Here, the subject is der Polizist. Even though he caused the bullet to move, he isn't traveling from point A to point B himself, so the action requires the standard helping verb haben.

I remember Polizist sometimes takes an -en ending. Why is it just Polizist here?

You are thinking of N-declension (weak nouns). Masculine nouns in this group, like Polizist, add an -en in the accusative, dative, and genitive cases. However, in this sentence, the policeman is the subject doing the action, so the noun is in the nominative case. The nominative singular form does not get the extra ending, remaining just der Polizist.