[pdonis]

> When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?

Relative to a local inertial frame, i.e., relative to an inertial observer (i.e., an observer in free fall, feeling no force) who is at the same spatial location as the particle whose speed is being measured. That is the only context in which the concept of "relative velocity", as it appears in the "can't travel faster than light" condition, has any physical meaning.

All of your suggested examples attempt to compare "relative velocity" between objects that are not at the same spatial location. That has no physical meaning in GR.