It's too cliche for co-stars to date each other, especially if their characters are together. Let them have their own personalities, be their own people.
No, I don't think they should. From what I've seen in interviews and such, they seem good friends and they have been for years, and normally it should stay that way.
Yes they should totally date each other and then soon enough get married. I've see a lot of interviews and studied each and every movement of theirs and from what I see is that if they say they r like brothers and sisters well brothers and sisters dont look at each other the way THEY do. They r definately in LOVE :)