Voltage vs current vs resistance - did I understand them right?
Voltage is analogous to pressure. Water flow rate is analogous to current. Drag (due to narrow pipe or long pipe) is analogous to resistance. If you reduce the flow rate in a hose by stepping on it, you will also affect the pressure. Basically, you will increase the pressure drop across the restricted area. Likewise, if you add a resistor in series with a wire, you will affect the voltage on one or both sides of the wire as well as the current. Basically, you will increase the voltage difference across the area where the resistor was added.

For DC circuits, you can think of it this way: electrons entering a wire on one side push out electrons on the other side just like water molecules entering a pipe. I guess the difference is that copper pipe is always full of electrons. They can't leak out (practically speaking).

If you need to understand what happens when voltage or pressure changes rapidly, then look at it like this: pressure disturbances travel at the speed of sound, and voltage disturbances travel at the speed of light (the speed of light as measured in the dielectric material where the wave is traveling).

I don't find that there is any big problem with water analogies, but I think many people don't really understand how water flow works, so they carry that confusion over to electric circuits as well.

Anyway, it is fine to try to gain intuitive understanding. But you should try to internalize Ohm's law and make that your new intuition:
V=IR