The manual says that the car is not to be allowed to coast. Coasting (yes I know it's illegal), has been a way of life for many years now. Just as changing gears is done often unconsciously, so knowing when to slip out of gear - road ahead descending, or rolling up to a junction - is done without thinking about it.
What damage can be done to the car?
As Hopkirk says coasting uses more fuel in a modern car in order to not stall. If you go down hill just lift off then the momentum will stop the engine stalling and the injectors will add no fuel. Yes I do have to pay for fuel out of taxed income, who doesn't? I also have a pretty good knowledge of the ICE and myths like coasting etc. Can you tell us about other things you do to "save money" we may be able to help.
Changing into and out of neutral causes as much wear on the clutch as changing gear. When in neutral the clutch is still driving something even if it's just a lay shaft in the gear box so how can you save wear and tear by being in neutral and coasting.
I have heard that engines at tick- over use no fuel before, and I cant understand how it can be true. If the engine is not burning fuel, surely it will be stopped? Its the consumption of fuel that makes the engine run!