Yes.
1908
Remington's web site has a good model history section that will assist you.
The Remington Model 8 was manufactured from 1906 until 1936 with around 60,000 being made in .25 Rem., .30 Rem., .32 Rem., or .35 Rem. caliber. Value will vary upon condition and examination.
A Remington Mod 8 in 95% conditiion is about $500.00
They made them in four calibers. 25 Remington, 30 Remington, 32 Remington & 35 Remington. The 25 & 32 are obsolete, the 30 was still available in the 80's & the 35 is still available at your larger sporting goods stores. There are dozens of custom reloaders that will still supply ammo for any of these calibers.
The value of the Remington Model 8 varies greatly with its condition. On average, this gun sells for about 400 dollars to about 1100 dollars depending on that condition.
100-1000
Remington's web site has a section with history on each of its products.
I found hand loaded .30 Remington rimless for my model 8 at Buffalo arms co google it there price is 38$ box a 20
.30 Remington is a caliber (now obsolete), not an identifier of the manufacturer of the rifle or its model number. Not many rifles were chambered for that round, and, if a Remington, it may be a Model 8 which was made in the time frame you reference. Take it to a reputable gun dealer to be examined and appraised, as it was made in various grades which can generate serious collector interest. It could also be a Model 14 or 14 1/2 slide action
There is no Remington Model 35, certainly guns produced in CALIBER .35 Remington but lots of different models. I would suspect one of the most popular would be a model 8 or possibly a model 14 or 141. If it's a Auto it's probably an 8 or 81, if a pump a 14 or 141, off hand I can't think of other .35 Remington firearms.
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.