On a 5 piece maple neck I doubt it. Probably just a ding and some finish checking. The finish color behind the first few frets is a little odd though. If it was a headstock break and partial refinish I would be surprised.
I'm no luthier, but if it was me I'd try to find out whether that "stinger" paint job was common on that model from the factory. I remember reading that Gibson sometimes did that to hide things like mineral streaks, but repair people sometimes did the same thing to hide neck repairs. Definitely makes it harder to tell, though.
Full disclosure: I'm not a repairman nor a luthier (if you consider them different). Usually Gibson headstock breaks don't happen horizontally like that (I've never seen an exception) (If I'm looking at what you are). They usually go diagonally from the nut area on each side. Like I said though, there could be an exception. If you aren't having tuning problems, I'd have nothing to worry about, and like others mentioned, looks like crazing in the finish.
Probably not on a laminated maple neck, and as Walter points out, with such an old and brittle finish any crack or repair would show.
The black finish on the back of the peghead is common on vintage Gibson archtops, my '63 Barney Kessel has it, although it's a 1-piece mahogany neck. I believe the L5S had it too.
That stinger makes me suspicious, but I don't know that I have good reason. You could always hit the area with a UV light and see if you spot any discrepancies. As for the unlikelihood of laminate necks breaking, as much as I love that idea, Firebirds had 5-piece necks and a reputation for breaking just as bad as any.