Definitely cull/kill sick birds. We don't eat them here, although I have read of others doing so. Maybe in another time or place we wouldn't waste the meat, but for us it's not worth the risks that could come with a sick bird.
As far as the other bird, things may change when her friend is...
We cull here. Sick birds, or any with behavioral problems. I think of my flock as a whole first, and individuals second. I gotta do what's best for the flock. Keeping sick birds around ups the chances of more getting sick. I give mine a week or two before I make the decision, unless it looks bad...