1 - I paint all my clay so if I make a mistake I can just paint over. I wish I could help you more with this one!
2 - For fine details, I often use a toothpick. It works well for small dots of different sizes. I also have a tiny paint brush that I use for pretty much everything. Most of my work is pretty rustic looking, so I don't need super fine details very often. Again, I'm not helping much!!
3 - Let your pieces dry over night or for at least a couple of hours before you glaze them. Don't be impatient!! I have never had a problem with paint smearing, but I always wait for everything to dry fully before applying glaze. That also goes for each layer of paint - before applying the next coat, WAIT, even if it's super fast dry paint, you should wait. I think it makes a better piece in the end.
It often takes me 3 days just to paint one charm, because I do it in steps. The way I see it, there's no point in rushing it if your risking loosing your entire piece. Patience is key!