The release of calcium ions at the axon terminal is responsible for the exocytosis of vesicles carrying neurotransmitters. 

When an action potential reaches the synapse, choline enters the neuron. Once inside, the choline molecule binds to acetyl-CoA and forms acetylcholine, which is then packaged into vesicles. Upon calcium influx, the acetylcholine vesicles fuse with the synaptic membrane and release acetylcholine into the synaptic cleft. The acetylcholine molecules can now bind to receptors on the postsynaptic membrane and initiate an action potential in the postsynaptic neuron.

There are two types of synapses: electrical and chemical. Electrical synapses have gap junctions between adjacent cells and are usually found between cardiac muscle cells. Chemical synapses are more abundant and utilize neurotransmitters (such as acetylcholine) to transmit signals between adjacent cells. They are typically found in neuromuscular junctions of skeletal muscle cells.

Acetylcholine is a neurotransmitter found in neuromuscular junctions. Release of acetylcholine into the synaptic cleft allows acetylcholine to bind to its receptors on the muscle membrane. Once bound, acetylcholine activates a signaling cascade that eventually leads to muscle contraction. Circulating antibodies in Myasthenia gravis patients prevent this interaction between acetylcholine and its receptor, thus decreasing muscle contraction. One way to treat this disease is by administering drugs that increase the half-life of each acetylcholine molecule. The most common way to do this is by administering an acetylcholinesterase inhibitor. Acetylcholinesterase is an enzyme that breaks down acetylcholine molecules in the synaptic cleft; decreasing or inhibiting this enzyme will lead to increased acetylcholine concentration. This increased concentration will compete with the antibodies and facilitate muscle contraction. Decreasing calcium influx in the presynaptic neuron will decrease the release of acetylcholine into the synaptic cleft. This will make Myasthenia gravis symptoms worse.

Out of all the neurotransmitters listed, the only one that isn't a catecholamine is serotonin. This neurotransmitter is initially derived from the amino acid tryptophan, whereas the catecholamines are derived from the amino acid tyrosine.

Dopamine, norepinephrine, and epinephrine are all catecholamine neurotransmitters. In fact, in the metabolic pathway that produces these compounds, dopamine is an intermediate that can be converted into norepinephrine, which can subsequently be converted into epinephrine.

Transferases are not neurotransmitters and can be omitted from selection. Catecholamines and small-molecule transmitters are overlapping categories and are typically packed in small, clear core vesicles. Gasotransmitters are membrane permeable and do not require vesicles for release. Neuropeptides are unique in that they are large and are synthesized at the ER, and are packed in large, dense vesicles, and thus this is the correct answer. 

An influx of calcium at the presynaptic terminal is absolutely required to activate fusion of vesicles with the membrane, and therefore release of their contents into the presynaptic cleft. Given that the specific deficit in these mutants is at the final stage of fusion, we know that the action potential propagated (so it's likely not sodium or potassium) and the presynaptic membrane is not responding to the voltage change to permit an influx of calcium. Therefore, voltage-gated calcium channels are the likely cause of this deficit. 

Neurotransmitters are found in the synaptic cleft; hormones travel through the bloodstream. Endocrine signaling is much slower than synaptic signaling, but hormone receptors have a much higher affinity for their ligand, than neurotransmitter receptors do. The highest speed of nerve cell electrical impulses is somewhere around . Neurotransmitters are localized around the synaptic cleft; hormones are dispersed in the blood.

The absolute refractory period during depolarization is the period in which it is impossible for another depolarization to occur.  The reason that another depolarization can not occur is that the voltage-gated sodium channels are inactivated.  This renders them unable to function, and also unable to receive any signal to activate again.  If the channels were closed rather than inactivated, they could still receive electrical input to open again.

After acetylcholine is excised from the presynaptic neuron to act on its receptors in the postsynaptic neuron, it is removed from the synaptic space by the enzyme, acetylcholinesterase.  Acetylcholinesterase breaks it down into acetate and choline which can then be removed.