Can electricity flow both ways? Can electrical current flow both ways at the same time in the same wire? If so, what are the drawbacks or complications of it?
 A: No, you cannot have multiple currents flowing in different directions in the same wire because all real wires have resistance. It will lead to inconsistencies with respect to other considerations, such as power dissipation.
To illustrate, see the circuit below. Applying Kirchhoff's voltage law for the two loops solves for the two loop currents $I_1$ and $I_2$. Note that current $I_{1}=4A$ flows from A to B through the 6 ohm resistor whereas $I_{2}=5A$ flows in the opposite direction from B to A through the 6 ohm resistor. The loop method allows us to determine that the actual current in the 6 ohm resistor is 1 A flowing from B to A.  The resistors shown in the example can be resistor components, or the resistance of wires (though they would likely be low resistance).
Although this technique is useful in circuit analysis, there cannot actually be two currents flowing in the 6 ohm resistor at the same time. Because if there were, both would be dissipating power in the resistor since the direction of current flow does not affect power dissipation in a resistor.
In this example, since the actual current flowing in the 6 ohm resistor is 1 A, that means the power dissipated is $I^{2}R=6$ watts. If there were actually 4 A and 5 A flowing at the same time the power dissipated in the resistor would be the sum of the power of each, or 246 watts, which of course is not the case..
Hope this helps

A: Charge carriers can move arbitrarily, but current density is the net movement of all charge carriers at a given point. So current will only ever point in one direction at a time at any location. That current may represent the net movement of many individual charge carriers in different directions.
A: It is quite possible to have a net current of opposite direction in different locations of a wire. An example is a wire that reflects light under an angle. There will be a phase difference related to the angle, the wavelength and the distance between the locations, which can be an odd multiple of $\pi$.
A: It is easy to perform a simple experiment that demonstrates the passing of two different DC currents flowing in the same conductor at the same time. The crux of this is that the conductor must have a resistance lower than any of the other conductors in the circuit and 2 separate sources of EMF be used. The flow can be proven using an DC amp clamp meter and voltmeter.
