Yes, the 4 was faked. It isn’t the same size or shape of what the 4 on the stamp should look like. Also, the left point wouldn’t fit within that space, hence the convenient leaving it off. However, the up and down of the numbers would be fine since it should have come from the same stamp if it were real.
As for the letter groupings of the hospital, that would be pretty much the same as it could have come from the same typewriter and the same typist.
That said, it’s not worth the paper it’s printed on.
Everything was faked. The entire document is a complete fabrication.