ethanol burns relatively cool (as do (some of?) the other alcohols). the problem is that it often burns above the ignition point of its carrier substance, which itself burns much hotter. e.g. calcium acetate/isopropyl alcohol gel (lab sterno) is perfectly safe to burn in your hand, but only until the alcohol runs out--it will light the calcium acetate, which is not remotely safe to burn in your hand.
hand sanitizer is usually an alcohol in water and a thickener (glycerin, etc.). i'd worry a bit about the same effect. (not that i actually know what the ignition and flame temps of glycerin are....)
Yes. And a virtually incandescent flame. I too burned just about every household chemical I could get my hands on. I remember trying to light my name in fire on the concrete floor of our basement... Good times.
