My first character is more of a destruction/one handed type and I'm not planning to use my arrows too much. But dragons force me to use arrows.
Can I fight them with swords too?

I dont see why not. Although, you have to worry about their breath. Whether it be fire or frost you are going to take some damage if you get too close. Depending on your play style, and where you encounter the dragon, you can get it distracted by say a giant, or some town folk, then hit it from the rear or the side. You say you are into destruction. You can use your fireball from a distance. It works especially well with the dual wield and stagger perks. I like to use that and arrows.

Once they land, yes. If you stand behind their wing and hit them in the back leg, you can usually do fine. It was a LOT easier before they broke the elemental resistances, but it's still quite possible.