IIRC a few nations kept some of them, and a LOT fell through the cracks (a lot for nukes anyway; the percentage was very low).
I doubt there would be much interested in keeping them; it requires a fairly high and specialized tech base to keep them operational.
That's correct. I believe Ukraine still possesses a few.
If they do, then not legally. It was a part of the separation deal in 1991: Ukraine could keep a big proportion of the Black Sea Fleet if they agreed to hand over all nukes. Which they officially agreed to.
Of course some of the nukes which fell "through the cracks" might in reality be kept back by Ukrainian or Kasach government, but I doubt it.
I have read somewhere (can't bother with looking up now) that most of the nukes that were considered lost during the breakup of the USSR actually didn't exist at all - they were a result of sloppy accounting, e.g. old warheads being sent back for recycling/renewal (decay and all that) but still remaining on the books of the respective unit because somebody was to lazy to do the necessary paperwork right.
To be sincere, it is a far likely explanation (for me) than nukes being illicitly traded around. If they were, I would assume they would have popped up somewhere already.