In Winchesters serial number block- 5,549,922 to 5,834,618 some of their Receivers were made by Underwood, and were marked T or AW below the serial number, often on the rear tang..... forward of the recoil plate.
"One questions I have is that it has a Underwood barrel Rough (the barrel is not smooth)"
The outside of the Underwood barrel has raised milling grooves from when being turning, common on all Underwood barrels.
Sometimes a worn die stamp left a light or nearly missing month stamp, or part of the year date.... So yes fairly common.
During WWII production Winchester DID NOT use Underwood barrels.
A Underwood barrel found on a WRA would have been a replacement barrel.
Underwood stopped making carbines in April of 44 (4-44) but did continue to build and supply replacement barrels as a sub contractor and was 1 of 2 Prime carbine makers to get a post WWII rebuild contract, their rebuild mark was stamped usually on the left side of the stock... looking like this: .U.
Any Underwood barrel dated past 4-44 was a replacement barrel.
Look closely for a Month Date stamp.
Look for any type of rebuild stamp on your Winchester stock..... Like RIA over EB in a box, or AA, AN, BA, MR, OG, RA, RRA, RIA, SAA, SA..... etc.
Sounds like you've run across a CMP rebuilt Carbine.
Enjoy it and take some pictures.
Welcome to Milsurps....
Cheers
Charlie-Painter777
P.S. I have a WRA 5,811,227 Serial number was stamped Oct 10 1944, probably completed by the end of Oct.