Does each sentence have a verb in it?

Yes.

A sentence is a group of Words, usually with a subject and a verb, that express a statement, question, or instruction. eg Jon ran. Did Jon run quickly?

Some sentences don't have subjects in this kind of sentence the subject (you)

is implied eg

Sit down. Be quiet. Pass the butter please.

If I write something like this -- Jon quickly to school (no verb) you can see the sentence is not complete.

Jon biked quickly to school.