All planets orbit the centre of mass of themselves and the local star, modulo interactions with other planets. The position of the centre of mass relative to the surface of the star is completely immaterial.

NB for smaller bodies, Jupiter is involved in perturbing or capturing their orbits to a great extent -- but we could conceivably have several very large planets contributing to that dynamic. Yes, Jupiter is the largest planet.

They are the two most massive, so that is tautologically true...

The contribution of Jupiter to the overall solar system barycenter is about the same as that of Saturn and Neptune combined (see numbers in https://news.ycombinator.com/item?id=14576751 ). So I guess it depends on how you define "main"....