Sniper Rifles
First off, I don't mean any part of this to be a personal attack, Zakalwe. Having ready the descriptor package for your proposed weapon, I've found that numerous design features integrated into the weapon are either a)non-sensical and inconsistent with ballistics and sniper roles, b)superfluous, or c)both.
We'll begin with your first paragraph. You're essentially designing a long-range railgun system for use as a sniper platform; itself made to fire 'a extremely sharp bullet'. First off, let's consider kinetic energy here. Your 'extremely sharp bullets(!?)' won't transfer a lot of it to their targets. In fact, the chances of overpenetration (the bullet going clean through the target without doing significant tissue damage) are more a certainty than just 'likely'. Your (normal) bullets will not likely deform unless they contact military-grade armor plating of sufficient thickness or something of the sort because of their construction material so the risk of accidental overpenetration is very high. I sincerely hope you didn't intend this weapon to be used in hostage or urban situations.
Your second bullet design which calls for "a soft outer layer so it doesn't ricochet, with a core denser than the standard bullets for maximum penetration, coming to an even sharper point than on the standard bullet, and on the inside of that an oxygen ignited explosive" is downright cryptic to even figure out what the damn thing does. From what I can figure, you have a penetrator, which is for some reason hollowed, surrounded by a 'soft outer layer' which I'm guessing means you have an ostensibly frangible bullet...with a penetrator inside it...which itself is carrying a small explosive charge...and is 'sharp'. What the hell sir. What the hell, is my only response to that. I truely do not mean this as an insult, but it's just mind-boggling as to why anyone would want a round of ammunition that is in itself contradictory to whatever mission purpose you'd find to even have cause to deploy it.
"It actually has two power settings, one that simply uses the entire force of the rifle, and therefore delivers an extraordinarily powerful hit, although by breaching the sound barrier several times over there is a very noticeable sonic boom, and a lower setting which fires the projectile at a fraction under the speed of sound, allowing for silent hits."
'Extraordinarily powerful hit'? It'll send your needle-round punching through the target and most anything and everything else behind it until the round's kinetic energy is dissipated, but I'm not entirely sure if that counts as an 'extraordinarily powerful hit'. More than likely the round will cleanly lance through the target (and probably cauterize the wound going through due to friction) without doing significant trauma to tissue or even material. There would be multiple sonic booms as your round goes hypersonic and their sonic signatures would be roughly analgous to what you hear today as the crack of gun (which is pretty much the round goin supersonic). Given the speeds tha the round is fired at, I assure you that your needle will have already poked your target long before they hear the sonic boom. If anything, I'd be more worried about the plasma rings the round would generate as it exited the barrel of your weapon.
Then, there's the subsonic mode. A good idea, we have 'Whisper' subsonic loadouts in the real world which do this. However, the Whisper rounds compensate for the lack of speed (thus allowing them to be more affected by environmental conditions) with slightly added mass so they have more forward inertia. Your needles, fires subsonically, wouldn't come close to the necessary MOA's needed to be considered match-grade ammunition as they would be too vulnerable to drop and wind.
"The laser sight connected is ultraviolet, making it invisible to the human eye spectrum."
Why ultraviolet? Unless you can see heat gradients, infrared is just as invisible to the human eye and since a laser is about directed energy then it would show up better as IF as opposed to UV. UV is just silly unless you want to sit there for a while, shine it on your opponent, and give them skin cancer.
"The rifle also has a reasonably powerful computer in it, which is capable storing personal information and comparing it to the target in the rifles scopes."
Snipers already have a computer like this. They call it their brains. Part of sniper training, especially in marksmanship, is target identification. Your computer just adds more unnecessary weight to the platform and, unless it powers itself through magic or something, is probably putting a load on the energy system that it doesn't have to.
"The amount of bullets left, and the number of charges in the battery yet to be expended, are on LED screens on the top of the rifle, and also in sniper scope."
Ditch the LED. If your scope also functions as a HUD, you're golden as it is. If you're in any situation where you're firing your rifle rapidly enough that you aren't using your scope and that you need a LED to tell you how many rounds you have left, you're not a sniper anymore and you're not using the right gun for the job.
Apart from those considerations, the gun seems fine.
And some closing thoughts on the idea of 'sharp' bullets: