In emergency situations many people press clutch and brakes at the same time, however if lets say we only press the brakes to still keep engine braking active , would that help us stop faster? I imagine engine braking also uses grip of the tires right? So if we dont use engine braking we have more working room or working grip for disc brakes so we can be harsher on the brakes themselves so engine braking wont be very useful, is this correct?
No, it does not, at least not in a car that has a properly working braking system. In every modern car the brakes are capable of locking up the tires on both the front and rear axles. Today that doesn't happen since most vehicles have ABS but nothing you can do will cause the car to stop any sooner since there is only a limited amount of friction between the tires and the road available.
The only thing engine braking does is take some of the load from the brakes but that will not, under most circumstances, cause you to stop sooner.
A possible exception is when the brakes are overheated and fading. In that case adding engine braking will help.
In fact the opposite - it will take longer to stop with the clutch engaged.
On a manual drive [stick shift] you would get some slight engine braking in 4th gear at maybe 40mph+, but if you were coming to a controlled stop at lights/roundabout by the time you'd slowed to maybe 30 you'd be dropping down through the gears to get a little more braking, maybe down again as far as 2nd, if you're polished at it. This is well worth learning, but learning to do properly. Clutch replacement is much more expensive than brake pads ;)
If, on the other hand, you slam all on in an attempt to come to an emergency stop, that 4th gear engine braking will rapidly tun into a gentle, but nonetheless positive acceleration force . It would only return to a braking force if you managed to slow enough to stall it dead - too late to have helped you stop.
You may think this is marginal, because of course the brakes are perfectly capable of actually stalling the engine, but all the time it's trying, it's wasting the energy it could be using to stop the car, stopping the engine as well.
Hitting the clutch simultaneously with the brakes removes that uncertainty & everything is then on the brake pads & ABS, which will not only be smoother but safer. They're designed to take it.
Only ever try to use the gears in an emergency brake fail or fade situation.
 You can test this [gently, don't try to accelerate from this] on a slight downslope by seeing what speed the car is comfortable at in top gear with the engine just ticking over at 700rpm or so [same revs as it would naturally do at traffic lights, in neutral]. That's the speed it will try to maintain if you don't engage the clutch.
 If you do ever have to use the gearbox alone to bring you to a rapid halt, you need to be getting down through the box as fast as you can. Each downshift will be from slightly too fast, so by the time you've brought the revs back up to match you're already in need of the next gear. This will not do your clutch one bit of good, because best retardation is achieved without rev-matching, it's using the clutch as a 'brake pad', so reserve it for emergencies only.
In all this I'm pretending cars still have just 4 gears - adjust according to your box. Mine has 7.
It can be argued that this question pertains more to driving technique than any vehicle maintenance and repair type question. I will however attempt to answer it as asked.
Personally, I was taught that during an emergency stop I should depress the brake pedal first and only press the clutch once the majority of the vehicle speed had been scrubbed off. Furthermore, in performance driving and motorsport application, you an not only taught to keep the clutch disengaged but encouraged to shift down the gearbox as the speed reduces, even under the hardest of braking.
Engine braking does depend on a number of factors including the type of drive train, type of engine and in the case of combustion engines, the weight of the flywheel. Some vehicles will show a dramatic slow down just be closing the throttle, others not so much.
In terms of available braking force, the combination of the maximum brake force available from the brakes alone will always be less than what is available from the brakes and engine braking.
One additional benefit of not depressing the clutch immediately is that the vehicle will be more stable than with the clutch engaged. Under emergency braking, it's more likely that your vehicle will "wag" it's tail. Engine braking counteracts this.
My final thought on this is in a cadence braking situation, where you either have to manually reduce pedal pressure because you've locked a wheel or the ABS does it for you, if the clutch is engaged, for that split second that the brakes are released the vehicle is in a free-wheel situation whereas with the clutch disengaged, engine braking is still active even for the time when the braking system is not.