I was told that I needed to replace the rear right hand side brake caliper since there is a lot of break dust + noise coming from that side.

The shop also told me I needed to replace the rotor since the calipers probably wore down a bit of the inner rotor. Total BS?

Correct me if I am wrong, but aren't the rear rotors solid and not vented?

If it's warped, probably if it can't be turned true w/o getting too thin.
If it's under the min thickness, yes.