Yes - this firearm should safely handle today's 3 in. shells
$125-$175
410 is not a gauge. 410ga
It is likely a 12 gauge, but take it to a gunmith to have it checked.
about $100
Winchester
I believe that your Sears shotgun is a Winchester model 37A shotgun that was made for Sears Roebuck And Co,.
about $100
sears and roebuck offered the same gun made by Stevens co as model #101.10080 stamped searsand roebuck co on gun no Stevens stamp. I paid 75 bucks for a sawed off. don't really know but if sears sold it prbly not much
The value of a Sears Roebuck 12-gauge 101.100A shotgun is around $100. This depends on the the condition of the firearm.
http://www.histandard.info/PDF/Sears%20Shotguns.pdf
1949
$450.00