The answer is no for both questions.
3 Charges: because the quarks are in the triplet representation of SU(3)
8 Gluons : because the gauge bosons are in the adjoint representation, that has dimension 8.
These two numbers (3 and 8) are not a priori
related to each other, as you can put your matter fields in any representation (not only triplet) (but you don't actually do it for physical reasons).