A model 12 serial 562582 was made in 1920, however it's value is anywhere from 200 - 1200 being new in the box. For values over 600 the condition has to be excellent. i.e. 95%+ blue.
1915
RW is Remington Works, not part of the serial no. 1912.
1925, It's date code stamped - check related links for information on the Remington Society of America
That's a Model 12C made in 1913, in mint condition it's a solid $1,200 but value drops QUICKLY in lesser condition.
1913 Remington MINT 750.00 U.S.
Remington never made a Model 1905 22 rifle.
what is the value of a 1945 single shot 22
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1925, Remington started date code stamping in 1921 so there will be a month/year code on the barrel. You can find the details on the Remington Society of America under the Manufactured Date link.
Which model, what condition?
1$
It was made in 1929, you didn't mention what caliber probably 22 rf so with a octagon barrel it's a 12C (if it is a .22 WRF / REM SPl) then a 12CS. The value is greatly dependent on condition in mint condition as high as 1,200 drops to 1/2 that price at 90% and then drops quickly from then on.