Gravitational waves move at the speed of light, doubtful you can "look" at it. If it's that strong it'll just seem like a shake. Like an earthquake. Except it's the universe that's quaking.
That's an interesting question and it's quite possible the medium matters about gravitational transmission speed. I.e. the question is how is gravity transmitted. We'd need to know a lot more about the structure of subatomic matter & interactions to answer this one. As it stands, we have no theory of gravity at all at the quantum level.
I'm firmly of the opinion there's no "spooky action at a distance". All waves propagate gradually (if rapidly) through a medium, even if we decide to call that medium "vacuum" and define it as empty. Or more modernly, a "field". Waves don't propagate in nothing by definition.
If light speed was infinite. If sound speed was infinite. Or even if water waves were infinite, we'd never feel or see anything waving.
We feel a wave by seeing the differential effect of it propagating. Which requires speed with a detectable progression. Compression, decompression. Excitation, de-excitation.
So when everything is quaking, we detect it by neighboring regions not being in sync as to the direction, amplitude, phase etc. of where they're quaking at any given moment.
Just like with normal earthquakes. The ground is shaking. If everything atop shook in perfect sync, you'd miss the earthquake. But otherwise, you feel it, you're destabilized. Not in sync with the ground.
For gravitational waves, it's much harder for us to feel it without special, very sensitive equipment. Normally. But if it was strong enough, we would.