In which direction do electric signals flow?
If electric signals are the propagation of EM waves at close to c in which direction do these waves travel? In the conventional direction? In the direction of electron flow? In both directions?

&quot;Both&quot; directions, as well as an omnidirectional component.
The best example might be an Ethernet cable. A bit is represented as a pulse. To transmit this pulse, the driving chip puts one output low and another high briefly. If it left them like that, then a conventional circuit would be formed with current flowing in a loop between them through the termination resistor on the other end. However, it does not, it quickly (let's say one nanosecond) moves the drivers back to equal voltages.
This launches a rising edge on the positive transmit wire and a falling edge in the negative transmit wire. If you have a fast enough oscilloscope clipped to the wire, these will appear as voltages, but really they're a small EM pulse travelling down the wire.
Each pulse also radiates an EM wave outside the conductor. Because the wires are twisted together at a constant distance, the &quot;positive&quot; wave emitted almost completely cancels the &quot;negative&quot; wave emitted. If this wasn't done, you wouldn't be able to use your radio in the same room due to the EM interference.
The cable can be modelled as a chain of tiny inductors along the wire, with a ladder of tiny capacitors between the two conductors. Each inductor stores the energy of the incoming current change in a magnetic field, before re-emitting it forwards along the wire.
The general subject is called a &quot;transmission line&quot;. The effective velocity is below the speed of light, but not much (see &quot;velocity factor&quot;).

travel of holes that gets close to the speed of light

It's a bit more complicated than that. (I've not bothered to fully understand that myself!) However, I believe this is why NPN transistors (hole mobility in the P region) are preferred to PNP transistors (electron mobility in the N region).
One of these days I'm going to write a canonical article on why electrons are a distraction for learning about electricity. Electricity is fairly straightforward and follows some mathematical laws that can be analysed with basic calculus. Electrons are not little pingpong balls in a tube, they are weird quantum objects that are capable of appearing, disappearing, tunneling through solid objects, and are much harder to model properly.