No, it's not a narcotic. The term narcotic really only applies to opiates, but can be applied to other depressants and (legally at least) applies to cocaine, though that's really incorrect.
Neurontin is prescribed lots. It's used for epilepsy, anxiety, (for some) bipolar disorder. It's used for nerve pain, as well.
Lyrica is prescribed a little less often, being that it's scheduled. It's used for nerve pain, epilepsy, and anxiety.
they're pretty much identical in effect, but pregabalin is more recreational because while gabapentin's 'high' will disapear after a few weeks of use, pregabalin is recreational for a lot longer.
Sure, and Benzene causes cancer. Tylenol is a brand name, and this may seem a little pedantic, but it's not really proper to say that something contains Tylenol. That'd be like saying that my arm contains Hammilton. Or that my microwave contains GE. It's nit-picky, sure, but there are lots of products bearing the Tylenol name that contain other actives other than APAP.
Anyway, they can cause weight gain, swelling of hands and feet (water retention, I think).
Gabapentin is about as safe as marijuana. Overdoses of 32 grams have been survived with minimal support. As doses increase, less is absorbed, making it impossible to get more than X amount into your body.
edit: that's not a problem with pregabalin. I don't know if you can overdose on that. Not many things work the way it does.