None of the above.
Electrons are negatively charged, always. They do not become positively charged under any circumstances. In DC circuits they flow (or rather 'drift' at about 0.1 mm/s) only in one direction, from the -ve terminal to the +ve. In AC circuits they flow forwards and backwards in the wire, changing direction 50 times per second. They don't go anywhere.
Although the drift speed is so very low, the current (the amount of charge flowing past a point every second) can be high because there are an enormous number of electrons moving in each cubic cm of metal - about 10^23.
As the electrons flow, it is the energy which they carry which heats the wire and does useful work. The charge does not get used up. They pick up energy from the electric field which passes through the wire between the terminals. It accelerates the electrons, and they release this energy when they collide with something.
In Response to Your Comments:
- Electric Field running through the Wire
Yes, this is a difficult concept. I think you may not yet know enough about electric fields to understand my explanation.
Briefly, yes : when the switch is closed, an electric field stretches from one side of the battery to the other through the wire, no matter what the distance, at the speed of light. (Well, actually a bit slower.) This electric field drives the electrons to move round the circuit.
- Positive current in AC Circuit
When applied to current, +ve and -ve refer to the direction of flow, not the sign of the charge carriers. It is like +x and -x directions on the co-ordinate axes. You can be going in the -x direction even when x > 0.
Current is measured in Amps. When you talk about +120V you are taking about potential difference (PD), not current.
PD tells you how much driving force (or electro-motive force) there is between two points in the circuit. The signs again refer to direction : a PD of +120V from left to right is the same as a PD of -120V from right to left. The sign here tells you whether you are going uphill (+) or downhill (-).