With these new pictures, I don't see why it couldn't be an original Bucks County gun. It has the right style, carving, etc. But the big issue is the patchbox. I've never seen one similar to that on another bucks gun. I would think this one originally did have a PB, because the shape of the wood next to the butt plate, with the spring and opening rod, is the same or similar to others I've seen and as the one I own. That, and the cavity just looks old. The carving certainly has a Bucks look to it, though obviously some of it has been recut, I guess to have it show more prominently. Original Bucks, at least the ones I've seen have pretty shallow and narrow incised lines. Some of the carving looks untouched, with the gunky reticulated look in the lines, like up on the forearm.
A few things on Bucks rifles that aren't obvious or visible on this one, is that the wrist is somewhat egg shaped, wider than high, the forearm sides are pretty flat sided V shape, the muzzle cap is open ended, and the RR entry pipe has a long wide finale.
The rear sight is the right type
As for the patchbox, most have one, but some don't. Those that do are mostly side opening boxes, and that's where the makers name would be as well. I've never seen one with this sort of box, and that carving around it all looks new in the pictures, so I'm going to guess it's not original. The two new screws don't matter much, as there's a new screw in the barrel tang as well. If you could get the PB off of there, there might be a shadow of an original one under it. But I think you're going to have to live with what you have, in that respect.
I think it is an original, but if you take the lock out, and/or remove the barrel, the wood will tell the tale there.
John
