1. Voltage-gated and ligand-gated ion channels.
2. Voltage-gated channels open and close in response to membrane potential changes of the cell and ligand-gated channels open in response to the binding of chemicals, like neurotransmitters, to the ionotropic channel receptor. Voltage-gated channels are ion specific and ligand-gated channels are not. Sodium, potassium and calcium ion channels are examples of voltage-gated channels and acetylcholine channels is an example of ligand-gated channels.
3. Ionotropic receptors are activated by the binding of neurotransmitters to ion channels, while metabotropic receptors are G-protein coupled receptors. Metabotropic receptors involve a series of second messengers and ionotropic receptors do not use or form second messengers. Ionotropic receptors are involved in a short process, while metabotropic receptors are involved in a longer process with more steps.
4. Adrenergic: metabotropic. Alpha receptors are found in the phospholipase C system and beta receptors are found in the adenylyl system.

Dopaminergic: metabotropic. D1 and D2 receptors are in the adenylyl system, stimulation of these have an inhibitory affect.

Serotonergic: both metabotropic and ionotropic. 5-HT1 and 2 are metabotropic and 5-HT3 is ionotropic.

Cholinergic: muscarinic receptors are metabotropic and nicotinic is ionotropic (causes depolarization and activating postsynaptic potential).

GABA: ionotropic, causes hyperpolarization and inhibiting of postsynaptic potential.

Glutamate: both, NMDA, AMPA and kainate are ionotropic and mGluR1-8 are metabotropic.

5. EPSP is an excitatory postsynaptic potential that causes the activation of action potentials, e.g. acetylcholine and serotonin. IPSP is an inhibiting postsynaptic potential that causes the inhibition/suppression of action potentials, e.g. GABA receptors.   
6. The binding of neurotransmitters to the receptors will open calcium ion channels and calcium will enter the nerve terminal and vesicles. The calcium ion influx causes depolarization of the synaptic membrane, which causes the formation of an EPSP. This leads to the release of neurotransmitters from the vesicles and nerve terminal into the synaptic cleft.