It would be a different case, when your heel slides down and one can see a 1/2 inch of the sole of the shoe exposed. But when your heel seems to be in place but the toes stick out - just a little bit, does my statement hold true?
Yes. If your toes are OUT of the shoe, meaning they're hanging over the shoe, then of course they don't fit. Either they're too small or too big (if the sole is exposed) and you're trying to tighten yourself down in them.
It depends, I wouldn't necessarily say that means they're too small though. Heels need to be a little smaller than other types of shoes, otherwise your feet will slide around and you'll lose your balance or have a hard time walking.