If one is under water in a giant fish tank traveling at the speed of light towards a black hole and one simultaneously shoots a .45 ACP and a 7.62X25 (both with night sights) into said black hole, would the 7.62 exit the far side of the black hole before the .45?
Although Cheetos is a decent answer really....
No, nothing *exits* a black hole. Neither would exit; therefore it's impossible for the 7.62 to "exit [....]
before the .45".
Also, would one be able to see the night sights at that speed?
Yes. You and the gun held in front of you are both going at the speed of light, so the "relative speed" between you and the gun is a zero vector. So the light which *emanates* from the sights' tritium (remember, it's not a reflection, so the light doesn't need to catch up to it), back toward you, will still reach your eyes at the speed of light (relative speed between the gun and your eyes).
Back to shooting pistols underwater, you really need to shoot ball ammo, not hollowpoints, to prevent the water in the bore from trying to expand the bullet, putting outward pressure on the bore, which will bulge the barrel, or worse. As for functioning in a semi-auto gun, it may or not function, but if it's tuned correctly, it will function. Such as when the Glock 17, for example, is used underwater after installing the "maritime spring cups" specifically made for this purpose, as a replacement part.
Rifles underwater ==> NO. Kb. The water in the bore cannot displace fast enough.
As for "is this a good idea (pistols underwater)?". Sure, why not,
but only if your head is above the water while shooting. If your head is under with the gun, you will most likely lose your eardrums, and not hear a sound ever again. At least that's my understanding.