We see leptons and quarks possessing charges. Can there be charge in free space devoid of matter(neither leptons nor quarks or anything else)?
While gravity is a curvature of spacetime, electromagnetism can be viewed as a curvature of the $U(1)$ principal bundle:
This however doesn't mean that empty space has charge. Instead, charge is the cause of the line bundle curvature. Similarly, in general relativity, mass (or, more precisely, stress-energy tensor) is the cause of gravity described as a spacetime curvature.
No, charge is a property of a particle not a thing in its own right, so it is always associated with a particle.
In principle a charge could be associated with a massless particle, and perhaps you would not count that as matter. In practice no such particles can exist or we would have seen them in collider experiments.
In the Standard Model, the only way to have charge is to have a charged particle: a quark, an electron/muon/tau, or a W boson. All of these charged particles also have mass.