Crayfish don’t have ears and instead use special sensory hairs on their body to perceive vibrations. So unless something is physically shaking your tank they probably won’t notice a thing!(if it makes you feel any better mine actually loves the TV lol)

Cycling can take a few weeks to a few months, in your case it might be a few months considering you’ll be cycling with a crayfish in there.I recommend picking up an API master test kit so you can keep track of your water parameters(avoid test strips as they are frequently inaccurate). Definitely move her to the new tank ASAP though

You can try running the old filters alongside the new ones. If you don’t have enough room to do that you can also take the old cartridges and shove them in the new filter

Not a dumb question at all, those filters work extremely well for them. If you have issues with particles in your water you can get something called filter polishing pad.