As has been explained multiple times in the answers and comments to your previous questions you are confusing a physical property (energy) with the units of measure (joules). "... making the current move faster by using more joules ..." should read "... using more energy".
- What is voltage really doing? Is it making the current move faster ..., so is it just making current faster ...
Raising the voltage will, in a resistor circuit, increase the current. Current is the flow of charge so, for a given conductor cross-section, increasing the current must increase the charge velocity. The current, however, moves simultaneously all around the circuit the same way a bicycle chain moves all links in the circuit simultaneously.
- What is electrical potential, and how does it tie in with voltage?
As explained in my previous answer, "Voltage electric potential difference, electric pressure or electric tension is the difference in electric potential between two points." Voltage is electrical potential.
- Do voltage dividers limit current?
Voltage dividers are usually made of resistors. Resistors limit current.
And if so, how do you find out how much current is per volt?
Use Ohm's Law. \$ I = \frac {V}{R} \$.
- What happens when voltage is increased, does more current flow?
Use Ohm's Law. \$ I = \frac {V}{R} \$.
From the comments:
1) Why does the current only increase in a circuit with resistance?
I mentioned resistance as an example because they are linear. Other devices don't behave in a linear fashion; LEDs, transistorised circuits, constant current circuits, etc.
2) How does having more charges (electrons in this case -> amps) increase the velocity of the charges, and why would velocity increase the amount of charges electrons in a certain space rather than just speeding up the electrons?
To increase the amount of water going down a channel (the current) you have to speed it up or make the channel wider so that it goes at the same speed. To get more current through a point in a circuit you increase the current density (and therefore the speed of the charges) or you increase the conductor width and maintain the same density (current per unit area - measured in A/m2).