Engine braking throws away energy just like conventional braking; both will reduce your fuel economy.

Welcome, Techie. With modern fuel injected engines, engine braking will often put you into DFCO mode, whereas using the brakes may not. In DFCO the engine uses no fuel at all. As I said earlier in the thread, avoiding the need to brake, by anticipation and lifting off early gives better FE.

Hi
I "accidentally" studied this at Uni in the lab. Plain and simple, low revs rule for economy. It is that simple. Next you must not labour the engine but basically the highest gear you can comfortably get into is best. For the avoidance of doubt about ratios etc, on a manual car, that is the highest number on your gear lever!

I cannot say a speed for each gear as it depends on the car, the road (slope, up or down) & the need for acceleration but just get in a high gear.

Next, the most economical speed is an extension of this. It is usually the slowest you can drive in top gear, in your car, without straining/labouring the engine. There is no panacea here like in aircraft with "min drag speed". Min drag is stationary for a car so the slower you go the less drag. Hence the usually caveat as some cars with massively tall top gears might, just might be more economical in a lower gear at a lower speed.

As for engine braking, yes use it when it is convenient but brake pads are cheaper than engines. Anticipate and leave a bigger gap and you'll save fuel and brake pads.

Moving off on a slight downhill I will sometimes block change from 2nd, straight into 5th. Depends on the road conditions, traffic, incline and even the weather.

My dad used to shift 1-3-5 when there was no traffic to interfere with a very gradual acceleration. I used to skip various gears at various times depending on load weight etc. out of the 18 gears I had available. I pretty much always shifted around the middle of the sweet band so I ran in the 1000-1200 rpm range where others might be mostly in the 1250-1450 rpm range. I got 8.X mpg while most others were getting 6.X or so. I'm a believer in low rpm light throttle. My hero was always the tortoise not the hare.

I learned to drive, over 50 years ago, on a 3 speed manual. Years later I graduated to a 4 speed manual and the Jazz is the first car I ever had with 5 gears. There are just too many for my needs!