I’ve seen the barrel shoulder not fully “seated” to the receiver on quite a few late war guns, mainly BNZ and BCD codes.
The barrel was scrubbed of its markings (you can see the faint remnants of the barrel codes) and it seems clear that the rifle was “humped” with the intention of it being numbered for the mount. 100% like you said, that FP is fake. A terrible choice of fake FP punch for all the work put into this thing.
As to the legalities.. a bcd45 would not have a receiver serial originally. The barrel can be scrubbed and renumbered to kingdom come and it’s not illegal.