I've fainted a few times during injections. It's not "normal" exactly, but it's not necessarily a sign that things are terribly wrong. The last time it happened was just a few weeks ago, but fortunately it only lasted for about a minute or so and the needle didn't get moved when I slumped over. It's scary, but nothing terrible happened. I do have a pretty intense fear of needles, so I'm sure that doesn't help any.
The only things I've noticed for sure when I have fainted is that I was a bit dehydrated and had possibly let my blood sugar drop too low, so I'm betting that's the most likely explanation.
As for the left-over dosage...definitely keep trying to get ahold of your doctor. It's never happened to me where I also removed the needle before the full dosage was in. My instinct would be to use a fresh needle to administer the rest, but I would want to check with the doctor to make sure there wouldn't be an issue with injecting at a second site or in the same place twice. Good luck.