I got two somewhat simple questions.

1: I've noticed the damage stats of my weapons have increased from time to time. What increases the damage? Is it my skill, my level?

2: What does the attributes Stamina, Magicka, Health really do? Is it like this...? Have I missed something?
Stamina: gives more stamina, faster stamina regeneration, more carrying capacity
Health: gives more health, faster health regeneration
Magicka: gives more magicka, faster magicka regeneration

1) Skill, perks, and any bonuses from enchantments, gear, improvements, or alchemy.
2) That's all correct.

1. Skill and smithing will improve this. The better you are with one/two handers, the more damage they do.

[EDIT] Tale is correct on the other ways to up the damage as well.

2. I think you have this pretty much down.

Ah so the higher the skill I got the more damage my weapon will do? If so, thanks a lot for making this clear to me. I always wondered what actually increased my damage every now and then...