Here's what additional info I could find to answer your questions.
Reloadron: Under the rear sight should be the manufacturer and the "ine" makes no sense to me. [Same here. Preceding letters appear to possibly been polished off.] Below the manufacturer should be the serial number. All that assumes a GI Carbine not an aftermarket flavor. The serial number can also be tied back to manufacturer. The barrel should have markings just aft of the front sight. [I’ve been over the barrel with a magnifying glass. Not a mark on it other than a few scratches.]
Travlin: If you got this via the NRA around 1967 it cost about $25, and today is worth around $800, possibly more. [It came from a gun shop in California.]
The serial number is supposed to be behind the rear sight in plain view. Sometimes it could be in front of the sight, but I think it would still be on the round top of the receiver, not the flat part just in front of the sight as your photo shows. I'm not sure that is a valid serial number for a USGI gun. [Agree, but it’s the only number anywhere on the receiver.] If it is, then I think it is an Inland.
The adjustable rear sight you have was added later, and covers the manufacturer's name. [I may need to remove the rear sight if I can figure out how.] Shine a bright light at it from both sides and tell us what letters you see. [Even with a magnifying glass, I can’t see any indication on any stamping under the sight.]
The F on the stock is a P "proof" mark. [It is clearly an “F” and the only stamp on the stock. Also, the stock seems varnished, not oiled if that makes any difference.]
The top of the receiver looks like a brown bronze color. Is that real or just the photo? [It’s real. Appears to be patina and only on the top surface of the receiver that is smooth/polished. The sides and all other surfaces are “machined finish and appear parkerized.???]
All USGI carbine were made during WWII, but many companies made commercial versions later. We can get yours figured out with a little more information from you. [Possible, but I was unaware of any commercial carbines at that time.]
Kbob: The manufacturer's name and the serial number should be under that rear over hang of the rear sight. There should be a date and flaming pot mark on the barrel top behind the front sight on top. [No marks/stamps of any kind.] Most reworked M-1 Carbines also have an M2 stock which is a bit thicker than the original M1 stock and has a cut out on the left front edge of the receiver area for the selector switch. [Neither the receiver (or the stock) have any any selector lever cutout.] Draw numbers on individual parts will not conclusively tell you the manufacture of the receiver as parts were interchanged.
Ibmikey: Your photo of the receiver suggests by the color of the metal and lack of sharp stampings that it has been refinished. [Agree. The top surface of the receiver is polished smooth while the other surfaces are machined and black parkerized.] If there is no s/n or manufactures name under the sight then you probably have a "liberated" carbine with that info removed. It was common practice to re stamp the s/n in front of the rear sight when upgrading to the adjustable sight, I do not know of cases where only a partial number would be used. [The four digit “1771” is the only number on the receiver and I can’t imagine that being a serial number.] The other numbers you see are drawing numbers and have no bearing on the serial.
Travlin: We need some more clues Twiki. The operating rod and rear sight appear to have a Parkerized finish. [Yes.] The receiver and trigger housing appear to be plum colored, which is a form of bluing. [Only the top surface of the receiver. The trigger housing does have a very slight hough to it, but is definitely a flat black (or extremely dark gray) finish.] What finish and color is the barrel? Is smooth like bluing, or rougher like Parkerizing? [Definitely flat black Parkerizing for all other metal surfaces.] Is it black, blue, or grey?
Some GI barrels don’t have a date, but I think they always have the name of the maker unless it has been ground off. Are you certain there are no marks anywhere on the barrel? Look at the flat area near the receiver, and the piston housing. Also look for a P about half way back from the muzzle. Check the bottom side. [No marks of any kind, no P or anything else and no indication of any grinding marks, just the machining marks from manufacture.]
How did you acquire this gun? [Gun shop in California and unfortunately, I no longer have the purchase receipt.]
Thanks for all of your responses.
One thing I’m beginning to wonder about is if this could be a non-military, commercially produced carbine that was made prior to the GCA making serial numbers mandatory and using some military surplus parts. Possibly even a USGI receiver with the original stamping ground off the top that could account for the polished surface on the top surface of the receiver. After owning this carbine for almost 50 years, these questions are starting to become an obsession with me.