Not without endangering yourself and anyone else in the area. Stay with ammunition designed for the firearm you are shooting.
30 caliber
Mint 30 Remington what? Rifle? Model? Variation? (carbine?)
No. A 30 Remington is a rimless 30-30. The .30ar is a .308 size bolt face and I don't think your rifle would stand the pressure anyway.
Remington 30-06rifles are legal anywhere in the US that all other rifles are legal.
$500
There is no "Remington USA 1906" rifle although there is the Remington Model 8, which was introduced in 1906. This is a semi automatic rifle that was chambered for one of four possible calibers; .25 Remington, .30 Remington, .32 Remington, or .35 Remington. The caliber that your rifle is chambered for should be stamped on the side of the barrel, just forward of the receiver.
remington 740 fieldmaster . 30-06 caliber rifle
The 7mm Remingtonn is longer. The 30/06 has a larger projectile.
Depends on a lot of things. What caliber is it? Mine in 30-06 is a $1000. rifle.
No, they are readily available.
100-400 USD
250-450