The first time I did the Triage quest, I ran around like a mad man and was quickly pi$$ed to find that I didn't complete it. The next time I tried, I just stood in one spot, closer to the back and in the middle. Then, I simply spun and bandaged, spun and bandaged, ... Complete! - He teaches Mageweave and Heavy Mageweave.
As far as I know, the Runecloth and Heavy Runecloth bandages come from books, and in order to get passed 300, you need the "Is there a doctor in the house" book.