No, it is a .338.
True, it is chambered in .338 caliber for use against targets over 1 kilometer away.
no, the 7mm is .284 bore, the .338 is, of course, .338
Your question is a bit ambiguous, so I'll go with the notion you're referring to the longest confirmed kill by a sniper. That was achieved with a rifle chambered in .338 Lapua Magnum.
100-1000 USD depending on EXACTLY what you have, its condition, box, papers, accessories.
740.00 plus tax CAD
Short answer is Remington. But it is a mix of parts. The action is that of a Remington 700. http://en.wikipedia.org/wiki/M24_Sniper_Weapon_System The above is the Army sniper rifle. Gibbs used the Marine m40. In the episode you're referring to, the rifle Ari used was a Bravo 51, chambered in .308 Lapua. This rifle doesn't exist. There is a Bravo 51, but it is chambered in .338 Lapua. There is no .308 Lapua. The Bravo 51 is named "Kate" and the rifle is only available in .338 Lapua. This platform is available in other calibers, but have different names. The TV show mixed stuff, but it's just a show.
The most accurate I have seen was Weatherby's SUB-MOA chambered in 338-378 Weatherby Magnum. No it is the cheytac m200 intervention look it up on YouTube or the discovery/military channel.
AFAIK, Browning didn't make any rifles in that caliber.
300-500, maybe more. It all depends on who did it, what quality of parts they used, and when it was done.
please list the maker of your rifle to get a correct answer to your question.
Also known as the Arctic Warfare Magnum, and made by Accuracy International. The AWM is available chambered in 7.62x67 (.300 Winchester Magnum) and 8.58x70 (.338 Lapua Magnum). The L115 is chambered in 8.58/.338. The A3 model features improvements such as the ability to attach a sound suppressor, a monopod on the buttstock to improve firing stability, adjustable front bipod (vs. the original fixed model), a folding buttstock, and adjustable cheek rests.