1) Does the electron movement actually occur? Or is it just a transfer of energy?
Both in AC and DC, electrons actually move. The electrons do not move at the same rate as the energy transfer. It is important to remember that electrons are already filling the wire along its length. An analogy for electrical current flowing through a circuit is water passing through pipes.
Imagine a water pump attached to a loop made of pipes. The water pump can pump water around the loop and supply energy to the system in the same way as a battery to a circuit. Let’s say we run the pipes across the room to the other side and attach a turbine. The turbine is connected to a fan by gears. The fan will turn whenever water flows through it.
Let’s get everything off the table and just sit still. The fan will not start turning immediately after we turn on the pump for the first time. This is because it takes energy to transfer from one end of the room to another. If the pipes are already filled with water, however, the delay will be shorter than the time required for the water to move through the room. Instead, the fan will turn as soon as the pressure waves in water are applied by the pump. The speed at which energy flows through a water circuit is determined by the speed of pressure waves (also known to be the speed sound).
An analogy would be that the speed at which energy flows through an electric circuit is determined by the speed of electromagnetic waves within the circuit. This speed can be significantly lower than the speed of light (70-80%). The actual electrons don’t move as fast around the circuit. They move at an average speed of about 1 meter per hour in typical DC circuits. This is known as drift velocity: http://en.wikipedia.org/wiki/Drift_velocity
Also see Why data transfer across wires is so fast?
2) I was told somewhere that the direction in which electrons travel is not known. Is it true? I thought the electrons would move from negative to positively.
I don’t know what you meant when someone said that the direction of electrons was “generally unknown.” As you mentioned, electrons in DC circuits generally move from negative to a positive electrical potential. They could have meant that you can pick any electron and observe its velocity. It could move in any direction. This is because electrons bounce off each other and atoms in wires, which causes energy losses called Ohmic losses. At any moment, an electron’s actual direction is random. The average movement of electrons in any given direction is slow, however.
3. AC current is confusing to me. How can the electron flow change direction constantly?
When thinking about energy transfer with AC, remember that energy flows from source to sink at all times current flows. This is true regardless of which direction it flows. Let’s take a look at the fan connected to the water pump. The fan will turn and spin if water is pumped clockwise around the loop. The pump is sending energy through the pipes to power the fan. The water flow will be reversed if we turn the pump in the opposite direction. The fan will spin the opposite direction as the turbine turns. The pump is still sending energy through the pipes to power the fan. It doesn’t really matter which direction the water flow (current) flows.
Also see How electrons create current when the cycle is always in reverse?