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.