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..............................................
Impossible to answer without knowing who made it. Even then, there might not be any published sn data.
100-500 USD
$700/900.00
100-400 US Dollars
100-1000 USD or more depending on specifics
Old Model or New Model? It makes a big difference.