1) The nerve cell, also referred to as a neuron, has several parts that are important for its function in the nervous system. These parts are:

Soma - or a nerve cell body, contains nucleus and other organelles. It is also responsible for synthesis of neurotransmitter. 

Dendrites - are branching extensions from nerve cell soma. They get stimulated by other neurons and transmit the impulses towards soma.

Axon - a single extension that extends from soma to the target cell. Myelinated axon is surrounded by Schwann cells (myelin sheath) with gaps of nodes of Ranvier in between them. There are terminal boutons at the end of the axon where the synapse is located.

2) There are 3 main types of neurons:

Sensory neurons (afferent neurons) transfer information from the external environment to the central nervous system (CNS).

Motor neurons (efferent neurons) transfer information from the CNS to external environment, to effector organ e.g. gland or muscle.

Interneurons, or association neurons, process information in the CNS and transfers the information from one neuron to the other within the CNS.