I am not quite sure about the clown wrasse question, but I can certainly answer your second.
I have actually owned the other three fish that you mentioned, and from experience, they get large! For instance, my S&S puffer was 13" long, my picasso was 9" long, and the yellow tang was 7". They were large species to say the least. In addition, my puffer chewed on the yellow tang's fins quite often.
I don't think that you will have a problem if you add the picasso last. They are not territorial, but the tang is. Please add that one last so it knows that it won't run the tank.
More, that is a lot of LR for a smallish tank. You would need to maximize the swim area (remove some LR), so your fish would me happier. In addition, if you could, please try to get a bigger tank. The species that I owned would not be too happy in my 180 if they were still living. Please try to upgrade if possible.
Hope that this helped. Take care.