Enamel is the hard outer layer consisting primarily of calcium and phosphate (the white we see when we look into our mouth's).
Dentin is the inner layer, the bulk of the tooth and is made up of 70% inorganic materials, 20% organic materials, and 10% water (elephant ivory is solid dentin). When dentin is exposed we get sensitive or sore teeth.
Pulp is the core, containing nerves and blood vessels.
Cementum is the thin layer around the root; a bone-like material which connects the teeth to the jaw.
The definition of ORGANIC, for A level purposes, is compounds of carbon, excluding oxides, carbonates and carbides (I think - it's a while since my A level days). Anyway, in simple terms, INORGANIC is everything else.
Yes, basically it doesn't contain any hydrocarbon groups (i.e. containing hydrogen and carbon elements bonded together). Sodium, carbon dioxide, asbetsos etc are inorganic, but things like hormones, fatty acids and proteins are organic.