Regarding your second question, yes. And as we increase our number of gravity wave followed shortly by EM wave detections, I'm willing to bet that the difference between the two will become a very useful tool in the cosmic distance ladder toolbox.
For gravitational waves the same effect will happen, as the waves pass through matter with its own stress-energy that will absorb some of the incoming radiation and re-emit it. But gravitation interaction with matter is so much weaker that it would take a significant amount of concentrated stress-energy or order to have the same effect. Sparse matter in interstellar space is too diffuse to experience tidal effects even at the small magnitudes of gravitational waves.
Gravity cannot travel faster than light in vacuum traveling faster than light in a medium is possible and happens all the time in nuclear reactors for example.
Since interstellar space isn’t empty light can lag slightly behind a gravitational wave but it does not affect the ultimate speed limit of the universe.