Location. The Hellkite Dragon attacks the player on the bridge leading to the Undead Parish, although it makes a brief appearance when the player first enters the Undead Burg. It guards the bridge until it is killed.

Does the bridge Wyvern return?

The Bridge Wyvern is the official name of this dragon. As far as I know, it will never re-locate and will impede your passage on one end of the bridge or the other. On the first playthrough, the Wyvern has 2208 HP.

Can you kill the dragon in Undead Burg?

Yes you can indeed kill him, and you get 10 000 souls when you do. As far as being killed with arrows, unfortunately I could not get a clear answer. The consensus on the forums I've looked through seems to be that he'll get down to about half health, at which point he'll cover his head, seemingly healing himself.