As a matter of fact, yes! This YouTube video is probably one of the most amazing things I have ever seen, he measured the change in voltage traveling along a Y circuit, where one end is open and one is closed.

You can see the voltage “ripple” through both branches of the circuit, reflect of the ends of the branches, and eventually settle into steady state. There are limits to this way of thinking (for example, water can’t travel in the space between “tubes”, but electricity can), but it is a very good way to approximate it.

https://youtu.be/2AXv49dDQJw?si=Bu50bjG6jkt1ktSQ

Sort of, electricity and magnetism are two sides of the same coin, electromagnetism, so it's waves in the electromagnetic field with the wire acting as a wave guide. (as far as I understand)

Veritasium has a video that goes over this. It was pretty controversial at release but it gives a good overview. https://youtu.be/oI_X2cMHNe0

And why magnets work due to relativity https://youtu.be/1TKSfAkWWN0