First year 1909
If you mean the US Rifle, Caliber 30, Model of 1917, manufactured by Remington, these were produced only in 1917-1918.
Model 581.
I assume your single action is pre-war ? If so, then made about 1907. As to the caliber, check markings on barrel. that should give the caliber.......
manufactured by savage arms corp.utica.n.y.usa
Many shotguns & .22 caliber rifles manufactured before 1968 did not have serial numbers. This would include your Rem. 512
1919 depends entirely on condition $100-1,200
Date code on barrel, check Remington Society of America - manufactured date link.
Your Remington model 1903-A3 was made in the year 1942.It was chambered in the caliber 30-06.
1931
1913
1919
1920