The presence of potassium leak channels in the membrane allows potassium to drive the resting cell membrane potential nearer to its equilibrium potential than to sodium's.

The equilibrium potential is the electric potential that would exaclty balance the competing forces of concentration and electrical gradients. High potassium concentration in the cytosol drives potassium out of leak channels in the membrane, toward the extracellular space, but the inside develops a negative charge as a result. When this negative charge pulling positive potassium ions back in is enough to exactly cancel the concentration forces pushing potassium out, the equilibrium potential has been reached.

The sodium-potassium pump, or Na/K ATPase, is what restores ionic concentrations back to normal after an action potential. This pump is electrogenic, and active, using ATP to pump three sodium out of the cell, and two potassium into the cell. Along wtih the potassium leak channels, this keeps the potassium concentration in a cell high, and sodium concentration low.

The sodium channel being inactivated, via its inactivation gate, prevents a stimulus from initiating an action potential immediately after a previous stimulus.

During the absolute refractory period, this is a fact regardless of how strong the stimulus is. During the relative refractory period the neuron can be stimulated, but only by a very large stimulus.

Post-synaptic potentials are graded, while action potentials are "all-or-nothing". This means that the farther from the point of integration in a nerve cell an electrical input enters, the weaker its corresponding post-synaptic potential will be when it reaches the distant integration site.

In this way, post-synaptic potentials can be summed as a function of intensity and distance, while action potentials are always the same amplitude no matter from how far they travel.

Remember that an action potential starts with the diffusion of sodium into the cell. As more sodium enters the cell, more voltage gated sodium channels open up. This leads to depolarization of the cell. With a steady diffusion of sodium into the cell, the threshold stimulus will eventually be attained, and an action potential will be generated. It is the steady diffusion of sodium into the autorhythmic cells which results in an action potential.

An inhibitory post synaptic potential (IPSP) drives the post synaptic cell membrane toward hyperpolarization, and thus away from the threshold necessary to fire an action potential. As a result, the axon requires more stimuli in order to fire an action potential.

It is important to recognize that sodium is flowing into the neuron during depolarization. The area outside of the neuron is electrically positive relative to the area inside of the neuron, resulting in the negative resting membrane potential of the cell. This potential allows positively charged sodium ions to flow from a high concentration of positive charge, towards the negative charge in the cell interior. Because the sodium travels from a region of relatively positive charge to a region of relatively negative charge, it is flowing down its electrical gradient.

Due to action by the sodium-potassium pump, there is also a large concentration of sodium ions outside of the cell, relative to the small sodium ion concentration inside the cell. This imbalance creates a chemical gradient across the axon membrane. The opening of the voltage-gated sodium channels during depolarization allows sodium to flow down chemical gradient from high ion concentration to low ion concentration.

Voltage-gated calcium channels do not cause depolarization in neurons, but are integral to depolarization in muscle. Voltage-gated sodium channels are responsible for neural depolarization; there are no sodium leaky channels in neurons, as these would disrupt the resting potential. Voltage-gated potassium channels actively import potassium, whereas the sodium-potassium pump actively exports potassium. There is no such thing a potassium-calcium pump.

During depolarization, voltage-gated sodium channels open and allow a rapid influx of sodium ions. The membrane voltage rises from its resting potential of -70 mV to 35 mV. Depolarization is not associated with endocytosis of neurotransmitters. 

The answer is saltatory conduction. Saltatory conduction is the term used to define the process of action potential jumping described in the question. The other possbilities, while involved in the nervous system and its function, do not adaquately describe the process in question.