Doubtful. The .308 Norma Mag was a fairly short lived cartridge, and competed with Weatherby's own line of magnum rifle calibers.
Custom proposition
The 300 Weatherby Magnum is a long action.
It can only safely accept the 270 Weatherby Magnum if that is what it is chambered for. If you want to chamber it in some other caliber than get a new rifle. Just because two bullets have the same diameter bullet (270 or any other caliber) does not make it safe to fire it in your gun.
There is no such cartridge as a ".308" weatherby, only a .308 Winchester, interchangable with the 7.62 Nato. Once upon a time, Weatherby only made rifles in unique weatherby cartridge calibers, eg. .300 weatherby, .378 weatherby, .460 weatherby, etc. Now weatherby makes rifles in many non-weatherby cartridge calibers, including the .308 Winchester. Do not confuse a rifle manufacturer with the company name that may have introduced the cartridge in which the rifle may be chambered. To further get your head spinning, many cartridge companies make cartridges (all equivalent) in the .308 Winchester caliber including Winchester, Remington, federal, norma, and multiple European companies. The short answer is yes they are the same. If you see a weatherby rifle chambered in .308, (and not .308 Norma Magnum), it is a .308 Winchester caliber (Winchester rifles exist in .308 Winchester caliber). The weatherby rifle is most likely a weatherby 'Vangard' model (a cheaper line of rifles manufactured by weatherby). Top of the line weatherby model rifles are noted for their high prices, ornate stocks and high power weatherby calibers (the .460 weatherby magnum is the most powerful factory cartridge in the world, about 80% more muzzle energy than the .458 Winchester magnum, first sold in Winchester's African model 70 rifle).
1000-10000 usd
Depending on the rifle, 1000 meters +.
Possibly the .460 Weatherby Magnum, the .577 T-Rex, or the .700 Nitro Express.
50-1000 USD depending on specifics
ABOUT $1500. depending on exact model, condition, scope, etc,
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.
Norma makes ammunition, not rifles. Accuracy will depend on WHICH rifle is firing the .308 Norma Magnum cartridge. Many are Schultz and Larsen products, others are hand built conversions. Accuracy will depend on whether it is a target rifle or a lighter sporter grade rifle. The round has pretty much been bypassed by the .300 Winchester Magnum cartridge.
DO NOT DO THIS!!!! The OAL on the 7mm Mag is 2.5 inches and the 7mm Weatherby is 2.55 inches. SInce they headspace on the belt, and due to the freebore in the Weatherby, the 7mm Mag may chamber in the Weatherby. SAAMI lists the 7mm Mag/7mm Weatherby as an unsafe combination one will probably chamber in the other. DO NOT SHOOT UNLESS YOU ARE SURE YOU HAVE THE RIGHT AMMUNITION!!!!