Look at the date code on the barrel. Details on the Remington Society of America, manufactured date link.
All Remington starting in 1921 are date stamped with a letter code on the barrel (month/year) you can find the details and table on the Remington Society of America under the Manufactured Date link.
According to Remington, it was made in 1913.
Can't be answered without the sn.
1922, will be date code stamped see related links.
Probably 1932 but it's date code stamped on the barrel, see related links for information on the Remington Society of America.
1926, late enough it's date code stamped see related links.
75-275 USD
Look at the barrel code, information found on the Remington Society of America here: http://remingtonsociety.com/rsa/questions/barrelcodes
1925, it will be date code stamped on the barrel. Check Remington Society of America manufactured date page for table/details.
They month and year can be determined by the barrel code, all the details can be found on the Remington Society of America here: http://remingtonsociety.com/rsa/questions/barrelcodes
Blue Book of Gun Values