Part one: I've wondered and tried to figure that out ever since I first read your question, PrincessZula. I haven't been able to figure out if he had that mark before he fought Katara-- I see three possibilities:
1. He burned himself when he was lying on his side shivering in that cavern and he had to use his fire breath to warm himself up.
2. It's a frostbite/ice "burn" from when he took a nap in that nice little glacier Katara made for him.
3. It's a goof... although it was prominently displayed, so I kind of doubt this.
Part two: I noticed that, but I assume that it's because they are all ladies of the Water Tribe. Maybe it's a traditional hairstyle.
Part three: Darn. Good thinking! I didn't catch that one. I guess the writers didn't either, ha!

