What is the best strategy to save fuel? (see below)?

lower gear, it gives more torque.

we can make a good machine with afew fuel

look in the manual for your car and find out what rpm gives the highest torque value

your best fuel economy is at that rpm so use the gears to keep the engine turning at that rpm

generally the higest gear of vehicles is set to give 55mph so if you can find the rpm of highest torque, drive your car at 55mph in top gear and see what rpm ot is running at

use whatever gear allows you to maintain a constant speed at 2/3 throttle for maximum fuel economy.

higher gear using more throttle

Since every revolution of the motor represents a fixed amount of work that needs to be done (moving the valves,compressing the gasses in the cylinders etc.) It’s always going to be more fuel efficient at lower engine rpm’s with the same drive train speed provided all other things are equal. Such as the air fuel mixture remaining at an optimum level. This may not be true for old cars that are carbureted instead of fuel injected. Carbs usually tend to run a little rich at high throttle and low rpm’s. While it is true that the more powerful combustion that comes from a higher throttle position will flex the crankshaft,pistons and rods more as well as the primary transmission shaft and gear these parts of the motor are very strong and the power loss won’t be significant compared to the extra work needed to turn the motor at higher rpm’s.
Your best fuel economy will always be in your highest gear with the lowest possible throttle necessary to keep the car moving. However, since in your tallest gear you will have the least amount of torque for acceleration this is very often not a desirable thing to do. Also car motors are never balanced well at low rpms and you’ll certainly wind up breaking a lot of things like motor mounts and exhaust pipes if you always drove around like that.

Generally its the higher gear with lower revs.

However when it get so low that the engine is bucking, you’ll hurt the engine or stall if you don’t downshift.

if it is really steep, then use 1st or 2nd gear and tap the throttle lightly.