Does fast-charging affect battery life?

I'm wondering if the heat I hear about being generated before the charging rate slows down after 50% would have any negative impact on battery life. Would there be any benefit in using my multi-port charger for overnight charges when I am not in a hurry to charge the battery?

Also, I assume that the battery doesn't have any memory, and that there's no reason to break it in, fully discharge periodically, etc. and that it's okay to charge a little or a lot regardless of the current charge state. Is that correct?