Learn Dutch: Zijn jullie klaar met het project? - Are you finished with the project?

Klaar met is a fixed combination that means "finished with" or "done with" something. The word klaar on its own can mean either "ready" or "finished", but pairing it with met specifically means you have completed a task.

How would the meaning change if I used voor instead of met?

Changing the fixed preposition completely changes the meaning! If you ask Zijn jullie klaar voor het project?, it means "Are you ready for the project?" instead of being finished with it.

Could I ask Ben je klaar met het project? instead?

Yes, but it changes who you are talking to. This sentence uses jullie and the plural verb zijn because it is asking multiple people ("Are you all finished?"). If you are asking just one person, you would use the singular Ben je or Ben jij.

Why is it het project and not de project?

In Dutch, project is a neuter noun, so it takes the definite article het. Many words borrowed from other languages end up being het words, but it is usually best to just memorize the noun and article together as het project.