Actually, from what I've read, coasting in gear with the transmission pushing against the engine (assuming it's above a certain RPM) will not use any gas, whereas coasting in neutral will use gas. Now that I think about it, if you coast all the way down to about 1500 RPM (in my car) you can feel when the engine starts kicking in some gas, the car jerks for a second (much like when you coast and then tap the gas).
As for doing damage to the transmission while in neutral, I doubt it (but I'm no expert).