If my only goal for this bike was to just get it working and ride it, I'd do just that. That said, I plan to customize this one at some point, so odds are the fork's getting swapped out. Might as well, just about every other part on this bike's been swapped out already!
You could try a Schwinn fork but it may be a little longer than the original. With a straight fork take it for a ride and see if it rides in a straight line. You will most likely find the frame is fine.
The frame in the photos is a Murray built WFlyer. You can see the tubes near the head tube are not smooth like yours. I’m sure the head tubes and seat mast electro forged sections have stubs to which the tubes are welded and the joins often look uneven.
The last image shows the head tube section on a Chicago built electro forged Schwinn. Murray was doing this before Schwinn. You can read more about electro forging on the Sheldon Brown bike website.