The pistol is NOT original. With the serial number showing a manufacturing date of 1944, and the relief cuts in the frame behind the trigger opening, it is an M1911A1 frame.
However, the grips are the style (perhaps not original) of the original 1911 type arm. Most of the arsenal rebuilds - which obviously had to occur AFTER 1944 for this pistol - replaced grips with the then current reddish-brown plastic grip panels. So I'm suspicious of the originality of the grips. (Which is not to say I don't like them. They are classic and functional.)
All the U. S. property Armed Forces pistols had lanyard loops in the mainspring housing. The lanyard on the magazine was initially used during the early days for pistols issued to cavalry (with real horses in those days) so the magazines were not lost when reloading. I'm not sure when that type of magazine was discontinued, but not long into the First World War, I believe. However, there have been some manufacturers since then who make 'reproductions' of that style magazine for the historical reenactment market. But I do not think they existed during the Second World War or for some time after.
Img 1377 shows a partial roll stamp of what I think was a Naval acceptance stamp. Which may indicate the pistol was once issued to the Navy or Marine Corps. Whether before or after re-build is not readily discernable; since the stamp seems (from the photo) to be finished over, I would guess prior to re-build.
The British markings on the barrel are curious. "Tons" is a very British measure of proof pressure, but my understanding is this unit of measure was not used (on proofs) until after WWI. Also in rebuild, barrels were commonly, but not universally replaced with new barrels which would not have had a British proof mark.
The hammer is the wide beaver-tail sort issued on early, 1911 pistols. However, the grip safety, and the trigger are the later 1911A1 design. The slide stop has checkering rather than simple serrations, so I would expect it to be the early 1911 type. (I can't see the manual safety well enough to tell.) The slide and sights appear to be the 1911A1 version - which would correspond with the serial number on the frame. This however means less in regard to a rebuild pistol.
The finish does not appear to be 'used' in the normal scope of an issued sidearm.
It is an odd pistol, in terms of provenance.
Still I would be delighted to have such a pistol in my collection. I like curiosities. Not to mention the family attachment, I am sure you want to maintain it.
However, unless one can come up with more solid information (copies of records of rebuild and release from service) or proof it was issued to Audey Murphy or Field Marshall Montgomery, I rather suspect the commercial, collector, market price to be in the $1500 to $2000 range at most. Simply because it is not - seemingly - a pristine 'original' configuration pistol.
I suggest checking your late Step father's records and seeing if he left any notes on the pistol. They could be invaluable.
Yes, it is shootable. However, do NOT carry it about in a holster and wear off the finish and make sure to clean the arm well after firing. Use standard 230 FMJ ammunition and it will probably shoot to the sights.