The battery in a closed circuit creates a uniform electric field in
the wire, which pushes the electrons from the negative to the positive
The electric field in a closed circuit will vary depending on the work required per unit charge to move the charge between various points of the circuit. The work required per unit charge to move the charge between two points is the potential difference, or voltage, between the two points. Consequently, the electric field will only be uniform throughout the circuit if the potential difference between all points in the circuit is the same. And that is because the electric field between any two points in the circuit separated by distance $d$ is
The electrons clearly have more potential to do work the farther they
are from the positive terminal because they have more distance left to
cover, so why then does their electric potential energy not decrease
uniformly as they travel toward the positive terminal, but is rather
decreased suddenly, when they encounter resistors?
It appears you are assuming that the wires connecting the resistors in the circuit have zero resistance. Apart from the fact that, with the exception of superconductors, the resistance of wires is never actually zero, if they were zero resistance then no work would be required to move the electrons between any two points in a wire. That, in turn, would mean the potential difference $V$ between any two points in the wire is zero and there would be no loss of electrical potential energy. The only loss of electrical potential energy would occur in the resistors of the circuit.
If electric potential energy is not converted into heat energy, then
which type of energy is? I don't believe it could be kinetic energy
because current does not decrease through a resistor.
Electric potential energy is dissipated as heat in a resistor, but not directly. To explain:
The electric field produced by the battery exerts a force on the electrons in the resistor. The work the force does on the electrons gives them kinetic energy. Then the electrons collide with the atoms/molecules of the resistor giving up the kinetic energy in the form of heat. Then the electrons again acquire kinetic energy from the electric field which they again give up via collisions. So the electrons alternatively acquire and give up kinetic energy obtained from the potential energy of the field, so that overall, there is no net change in the kinetic energy of the electrons, which is why the drift current of the electrons is constant. The overall effect is the dissipation of electrical potential energy in the form of heat in the resistors.
Additionally, I do not understand the physical significance of
resistance. In other words, why is the resistance at a point in a
circuit defined as the ratio of the potential difference across the
point to the amount of charge passing through the point in a second?
Your understanding of resistance, potential difference, and current is inaccurate.
First, there is no resistance "at a point". Resistance is between points.
Second, there is no potential difference at a point. Potential difference is between points and, as already stated, the potential difference between two points is equal to the work required per unit charge to move the charge between the two points.
Third, current is not the amount of charge passing through a point. Current is defined as the rate of charge transport through a surface.
So your last statement of Ohm's law should read:
The resistance $R$ between two points in a circuit equals the potential difference $V$ between the two points divided by the rate of charge transport through a surface between the two points, which is the current $I$.
Finally, I know this may sound silly, but what stops the large
concentration of like charges in both terminals (positive and
negative) of a battery from repelling each other and therefore
separating, causing the terminals to no longer be charged?
The only thing that stops it is the absence of a circuit connecting the terminals to enable the charges to separate. In other words, the accumulated charge on the terminals have no where to go if there is nothing connected to the battery terminals.
Hope this helps.