If you have a relatively modern car you should not coast downhill because it will use gas while using the engine brake doesn't.
More, if you don 't use the engine brake you even risk overheating your brake fluid which believe me is not fun at all when you are going downhill.
Whether coasting (engine on) is good or bad, depends.
- If there is only a light slope to coast down (such that coasting will put you at or below the legal and safe speed), it is good. Yes, you will burn more gas while coasting as compared to being in gear, but you will slow down less and will not have to re-accelerate as early.
- On a significant slope (which sounds what was described here) where you would have to break if coasting, it indeed makes no sense. You will be burning the gas for no good reason and also using your brakes more than necessary.
Accelerating slowly is often not fuel efficient. The most efficient way of accelerating is with almost 100% throttle, shifting up as early as possible.
Cruising in high hear is good. Always be in the highest gear possible (i.e., where your engine makes no funny noises).
Coasting with engine off is practically never worth it. The savings are minuscule (my car for example uses only 0.7L gas per hour of idling). And many of your drive assistance stuff will not really be working. Most importantly the brake booster will not be recharged, after you have used it up.
On a side not concerning this: If you have access to somewhere away from traffic (and other obstacles; like a big empty parking lot), you should try to brake without the booster to see how it feels: Accelerate to a fairly high speed (maybe 80km/h), shift to neutral, shut down the engine, then brake abit, release the brake, repeat. In the beginning it will work like always (booster still working). But as soon as it has used up its vacuum, you will feel as if the brake is not doing
anything anymore. But it's not quite true. If you hit the brake with all the force you have, you will be able to stop the car, but it will take a bit. It's an interesting experience and knowing how it feels might save your butt one day, if your brake booster ever fails for any reason.