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Know facts:
Question:
When you car can brakes (maintain that maximum force without locking the wheel), does downshift together help to stop the car?
No. Your tires locking is based on the static friction of the tires to the road.
Once the static friction is overcome, regardless of whether it is from engine braking or normal braking, the tires will lock.
EDIT:
I'll expand this answer based on the edits.
Your tires locking is based on static friction between your tire and the road. Braking on ice will lock the tires much easier than wet asphalt, which is also easier than dry asphalt.
Your ability to brake is based on your brakes and engine braking, and other source of friction applied to the rotation of your tires. You can also do other (highly NOT recommended stuff) like put your gear in reverse, go into gear and shut down your engine, etc. Whatever it is that causes the wheels to not rotate as well.
Where the source of braking comes from don't matter. You simply want to get as close to the static friction limit as possible without exceeding the static friction limit.
EDIT
Brakes must be capable of locking the wheels (with ABS disabled). If the brakes can't provide this force, then there's something wrong. To brake effectively, you must regulate the brakes (or the ABS must) such that the force is just below the amount required to lock the wheel. This is done by intuitively understanding the vehicle's tell (pedal feel) by practicing threshold braking. In the case of ABS, sensors are used (wheel speed, G sensors etc) to determine wheel lock.
Engine braking definitely aids the brakes while braking. The known fact you've mentioned is axiomatic.
Now to your question as I understand it -
Is there any benefit in using engine braking (by downshifting) when your brakes are fully capable of threshold braking?
I would read from your question an additional doubt about threshold braking and would urge you to read up about it. Knowing how to brake hard is, i guess, one of the most overlooked skills in driving/riding (I'm not talking about pros). This here is an easy read.
Good brakes must be able to lock your wheel. To be able to brake most effectively (threshold brake) , though, you must apply (or the control system like in ABS must regulate) the maximum amount of braking pressure that the surfaces in contact (your tire is only half the story) can allow before the wheels lock. A tiny amount of wheel slip is beneficial, but that's another topic.
Using engine braking aids your regular brakes, and hence, quite simply, it takes some work off your brakes.
Engaging the clutch as soon as you start to brake isn't good practice-
Having said that, I would argue, for a non-professional, that for critical-emergency braking situations, it's best to concentrate on braking and steering without additionally thinking about downshifting. There is no additional stopping power derived from using engine braking while braking at the limit. Downshifting, if done incorrectly will have the tendency to upset the vehicle and even cause the wheels to lock due to abrupt application of engine braking.
No, if you apply additional braking force when the ABS is already active, you will only make the ABS work harder. You won't see an improvement in stopping distance.
If you're doing an emergency stop and you need to quickly trim about 2-5 meters off your expected stop, you can use the emergency brake while simultaneously jerking the steering wheel to one side when your speed is relatively slow (e.g. under 30km/h). You will slide sideways, losing momentum. This technique utilises the same theory that underpins trail braking (what experienced racers use to maintain speed coming into corners).
