Thinking about quail:question!

You can, provided you brood the chicks somewhere else for the first two to three weeks, since the chicks will happily walk through chicken wire.

Coturnix are perfectly fine in tractors. Be a little more vigilant about small spaces, since they can squeeze through smaller spaces than young Birdzillas. You probably won't have to move them as often, or will at least sill have to mow in the area where you've housed them, since they're not going to be as effective as eating and stomping down the grass as larger meat birds. Regular moving will probably still be a good idea to give them fresh access to seeds and unsuspecting insects.

If you raise them in a tractor I'd love to know the results compared to cage raising. I've never compared the weights.

Edited for spelling. Bleh.

 

Chickens can carry diseases that can be fatal for quail. The chickens may not display any symptoms.

If you are going to use any recently used chicken housing for quail, then you'll want to look up proper procedures for sanitizing the building / structure as best as possible AND be aware that there is some risk, however small, of disease transferring.