Until someone more knowledgeable responds to your question, here is my understanding. Quarks are inside of subparticles and cannot be directly manipulated. However, there is serious work going on to build quantum computers that, I believe, use quantum properties of electrons.

Theoretically, yes. You can use pretty much anything you can predictably change and read state from to form a logic array. The problem is doing so in a practical, cost effective manner.

What do you mean by “used”? Are you talking about data transmission, computation, storage, or something else?

@phaedryx computation

There is no theoretical reason why we couldn’t employ quarks in this way. Free quarks only exist at 10^12 degrees Kelvin however so there will be practical difficulties to overcome.