Downshifting to slow down uses zero fuel. Modern cars cut fuel completely when coasting is detected based on throttle position and whether gear is engaged among other sensors. This is only used a lot in manuals since the torque converter causes freewheeling at lower rpms. It's known as deceleration fuel cut and it's standard in OEM and aftermarket engine controllers.
Typically the engine "restarts" when rpm drops to a bit above idle speed but as mentioned it doesn't happen as much in automatics because of the freewheeling. In automatics it only occurs when deceleration starts at high rpm or the clutch within the torque converter is locked during steady highway driving. I assume shifting into "low" may enable deceleration fuel cut in more situations assuming the driver may be using it to slow down, but I have no evidence of that usage
No reference, but engine braking means you don't need to send petrol to the engine (since the engine is being driven by the car's momentum), so there should be no fuel usage. When the car is stopped, then it will use more petrol (to keep the engine from stalling). Assuming all things are equal, then when you brake with your foot brake, the energy that gets turned into heat in the brake pads could have instead been turned into energy that keeps the engine spinning (and so it doesn't need to come from petrol).
Basic understanding of an injected engine and power conservation should be enough here.
When you're downshifting you're braking with your engine.
This means two things:
1. Less fuel is burned. The injectors are closed while the engine is braking.
2. Momentum, not fuel, is used to drive the alternator, AC etc.
If you instead were to brake the car, it would need to use fuel just to keep the engine running. In the same way as it would if you were idling parked. Even more fuel is needed to combat the resistance from your AC and alternator.
Engine braking in most petrol cars is an efficient tactic due to DFCO[0] - less efficient than coasting in neutral, but you're not as in control of the car when not in gear, so the combination of both being in control and getting a "free" slowing effect (especially when judging upcoming traffic, as opposed to coming to a complete halt) can be better than just mashing the middle pedal.
If you're slowing down to traffic light, it's more efficient than coasting in neutral. You've to slow down anyway and slowing down with engine braking is 0.0l/km. While coasting still burns some fuel.
In addition to that, some newer cars charge battery when engine braking. Which is effectively saving fuel later.
Was taught to do it in drivers ed, which features environmental driving here. The point is not to aggressively downshift, but to let go of the gas and then downshift when the RPMs are lower. You still want to keep the RPMs relatively low. This is preferred to a situation where you would keep your speed and use the brakes at a later point in time. I should probably not have called it downshifting.
I had assumed engine-braking will heat up the engine more and use more oil and increase general wear on the engine and reduce it's service life. New brake pads seem cheaper and more environmentally sound than having the engine serviced/replaced and burning more oil...
You can downshift and use the motor for breaking. When doing that, you don't burn any fuel at all, as the kinetic energy of the car will help keep the motor turning.
You have the same effect in automatic transmissions when letting go of the gas pedal.
Because burning more gas is better than heating up break pads?
Reference?