The "Ranger" class in Dungeons & Dragons sounds a bit like this.
Dual axes + light armor, or 2H + light armor, makes me think berzerker. Barbarian fits better with archery, though. Depends on how crazy your character is. A barbarian might think about tactics. A berzerker should just rush in and let others worry about the consequences.
I'd call it AWESOME! I usually play duel wielding, archery characters. And Nords, to boot
Seriously, Ranger for the Duel Wielder and Barbarian for the 2-hander sounds about right if wearing light armor. A 2-handed heavy armor wearer would be more like a Berserker, in my opinion.
Sure. A smart one, at least. There will be flying opponents that they can NOT hit while on the ground, so I see no trouble with it
Arrows and hiding until they land. They are usually about 1/3 health by then. Quaff an appropriate elemental resistance potion and swing away
Sometimes, I will run to populated area with plenty of guards nearby to help me out. I have run from the wastes outside of Kynesgrove all the way to Windhelm for help
I'm playing the main quest with a Greatsword-and-Bow character right now. And I use the same tactics as AIBQuirky. I fire off arrows and use the terrain to my advantage. I do a lot of hiding and healing. The instant I hear a Dragon I begin searching for places where I can take cover and dart out for a second to fire off an arrow and then dart back under cover to heal.
I use a mod called Deadly Dragons which boosts the attributes and abilities of Dragons immensely. Dragon fights take over 30 minutes in my games and usually leave me so exhausted and frazzled I have to take a break to recover.
When they land, that is when I run up to them with my Greatsword. I try my best to stay out of reach until then. If I can.
Legolas. Pretty much what you're literally going for.
Well if you want to go historical, you need to use a http://en.wikipedia.org/wiki/War_hammer#Maul with your archer.