Don't worry about moving it now, it needs to settle in for winter. Mine are all yellow also at this point and it's just the cooler temperatures at night.
I do have problems finding nice Hostas around here, I have been doing mail orders for a few years and I know of some good companies. I posted pictures under my recommendations. Like I said choose sun tolerant Hostas and if you want to avoid some headaches get slug tolerant when ever possible. If you have something delicate that gets munched a lot you can always put it into a nice colorful pot and just sit it in the bed that way.
Yes you can plant them under trees as long as the tree roots are not in the way. I have a raised bed under the tree and that helps, Birch trees have awful roots.
