They are suppressors (a.k.a. silencers). They work just like your car's muffler and both were invented by the same guy: the grandson of the inventor of the Maxim machine gun.
It will certainly not make these monster guns movie-quiet but it reduces their massive sound and flash signature making it harder to locate where they were shot from.
Certainly looks that way. As if it wasn't big enough already. In most pictures I have seen they have only muzzle brakes, but in some they clearly have suppressors. A useful side-effect may be to reduce the visible muzzle fire for night operation.
Bullets are deflected along surprisingly sharp bends in a barrel (or any other pipe), so it would be sufficient to hit the tank gun muzzle roughly from the front, and it would probably hit a loaded projectile.
Technically, it would be sufficient of they lodge a bullet into the barrel. As soon as the tank fires, the bullet will wedge between the shell and the barrel, destroying - at least - the barrel.
Assuming a BC of 1.05--I'm using the BC for a match-grade .50 BMG bullet, which might be high--and using a 921gr bullet with a 3300fps muzzle velocity, you're going to see about a 13' drop at 1000y. That's pretty significant.
If you compare that to a .338 Lapua Magnum, .685 BC , 250gr at 3030fps, you end up with a 18' drop at 1000y. Also significant.
So it's a bigger, heavier rifle, and it will definitely go through body armor, but you aren't really seeing a huge gain in functional range, and the ammunition (since 14.5x44mm is an HMG bullet) is likely not nearly as consistent as .338LM and so likely not as consistent at long range.
BC - ballistic coefficient. How your bullet reacts to the air. It's a combination of weight and shape of the bullet. Higher is better for long-range shooting.
gr - grains. The weight of a bullet. 5.56x45mm (standard AR-15) uses bullet weights as low as 55gr, and as high as mid-70s. Lighter bullets are easier to push faster (which is why AR-15 rifles tend to be pushing bullets to 3200fps with pretty minimal recoil).
fps - feet per second, usually measured at the muzzle. Bullets slow down as they head down range, due to air resistance.
Bullets don't travel in a straight line; the second they leave the barrel, gravity is acting on them, and they're getting pulled down. So you're always shooting in an arc. For short ranges, that arc is pretty negligible. For a long range shot, you may need to be pointing significantly higher than your target. In the case of the rifle pictured, you should need to aim about 13' above a target that's 1000 yards away in order to have your bullet hit (that's your "hold over"). If there's wind--and there almost always is--you're going to need to compensate for that by aiming to the right or left ("windage"). A spotter makes this much easier; your spotter should be trainer to read winds. They should also be trained to see where the bullet hits, so you can make an adjustment, e.g., one target to the left, one half target low.
(I've only gotten to shoot longer range a handful of times, the last time with a spotter, and the spotter made it so easy to get on target. Check out 9HoleReviews on YouTube for examples of how that works with a really excellent marksman and spotter.)
Anti-materiel is it's primary purpose. For that 14.5mm beats the .338. The pictured weapons are for penetrating engine blocks that are stationary or moving with simple motion, within a greater effective range, not body armour (but will all the same). Long range extreme precision is secondary but is still a feature of 50cal and 14.5mm (top 3 records sniper kills are with a 50cal/14.5mm: #3 is actually with one of those type rifles).
You forget it's not a precision rifle, and it's not meant to be used against Infantry directly. It's accuracy isnt meant to be measured in minute of angle but instead minute of APC