According to Remington's website, that model was made 1928-1933.
The Savage Model 6 was Mfg'erd from 1938 to 1968.
Remington never made a "improved" model 8, unless it's called the Model 81 (an improved version of the model 8) however this gun was never (and couldn't be) offered in a 22, it's a center-fire rifle only. Either you have mis-identified what you have or the amount of gun-smithing done is substantial and like amazing if it works.
1929 to 1933 The Improved version of the Remington model 6 became available circa 1905, and featured a blue frame in 24 in. barrel. Production continued until 1933. The earlier models had the original case colored frame.
100-200
value depends on the pistol model, overall condition and serial number. If a good early model single action, value could be $1500 - 2500..............................................
$700/900.00
100-500 USD
100-400 US Dollars
100-1000 USD or more depending on specifics
Impossible to answer without knowing who made it. Even then, there might not be any published sn data.
Old Model or New Model? It makes a big difference.