1. Not much different than a Hobbit, though deformed through living way past his species' normal life-span and centuries of living in the caves under the Misty Mountains, away from sunlight.
3. Gollum is more insane than anything else, I'd say. He's gone for centuries obsessing over the Ring, being poisoned by its power and overwhelming malice. Though the bit of Smeagol (his original personality) still might exist somewhere in there, the greatest part of his personality is that of a creature undeniably and forever tied to this artifact he loves and covets beyond anything else. Though he never wants to use it in any grand scale (I don't think his cunning is great enough for that), he still has this desire to be the "Master" of his own little world, keeping his Precious Ring close so he can love, caress, and adore it. When you lose something that basically forms the core of your existence, it's bound to throw you off a bit mentally.
3. The idea (better expressed in the film), is that being judge, jury, and executioner is much too rash a path to take. Gandalf sums it up: "Many that live deserve death. Some that die deserve life. Can you give it to them? Then do not be too quick in dealing out death in judgment". It would be a shame to have killed Gollum, only to find out he may have had a purpose to the greater good later on. On another note, Gollum was such a wretched, sad, pathetic creature that people felt sorry for him, being in that state, and decided that killing such a thing would be too cruel.