Sorry so long getting back to you, It's getting so time consuming trying to read through all the postings now. First off on the fat guy, I don't think it is dropsy, worst case scenario IMO is it is possibly egg bound, If that is the case there isn't much you can do, it will either absorb them, lay them, or die from a internal blockage. Dropsy is not hard to tell, the scales stick almost straight out, the skin tone will be non shiny and pinkish in color and the fish other fish will start picking on it. I think it's a fish that mixed a fat body fantail and a long fin comet and that was the result. Just a fat bodied fish.
I've looked several times at all the pics, honestly I really think they are all goldfish. I've seen thousands and thousands of fish and I say that with pretty good confidence. BUT, on the side note that they are a butterfly koi or hybrid between the two, Your plants will be plenty fine for now. My pond is loaded with plants and koi, butterfly, standard, and goldies. the only plants they really mess with is the lettuce and hyacinths roots for the most part. you'll know long before they do enough damage if you need to get them out or not. The biggest concern I would have if it is in your pond situation is them digging in the pots. easy fix, if they do just get some rocks that are about the size of golf balls and place them on top of the litter, or whatever planting media and completely cover the top layer. If they can't pick it up in their mouths they won't dig in them. If you can keep them from digging that's where they do the most damage to lily's. yes they will nibble, but so do bugs and everything else.
now for the part on barbel's on butterfly koi, the Internet isn't really that wrong, The original butterfly koi was breed for long fins, there fore the barbels grew longer too, but in the more recent years breeders have been breeding More colors into the Butterfly koi, So some do retain the the barbels as shorter in some of the newer breedings, For instance if you look at CliffandJoannes butterfly koi you'll notice the side fins are shorter and stubbier, Fish that were breed when they got there's were probably from descendants of koi that breed 10 or so years ago, their barbels and fins are quite different from those you'll see on ebay these days, there fins are much longer and the barbels on most seem to be getting shorter on some. In the show circuit there is a breeder that breeds the kohaku, (which by the way if they are Koi, this is what your red and white would be called) his fish have very small almost unnoticeable barbels, he has been paying more attention to size and color and not wanting to bring out fish with barbels that distract from the facial appearance, yet there is a breeder in Malaysia that breeds for the opposite, he breeding very large barbels and big patches of broken color. This is a living art, very similar to dog breeding, breed back what is appealing to the eye breed out what is not. The show circuit fish are heavy body, Bold, equally spaced, color fish, Butterfly koi breeders are looking for massive body, they are looking for striking flashing color with long flowing fins. This is where your seeing Gin Rin and mettalics really being developed. In the future your going to see even more changes and new colors, I'm expecting the butterfly koi to start being shown more and judged more.
We are planning on going to the Dallas Texas koi show next month. They do have a class for butterfly koi to be shown. I'm interested in seeing what gets shown and if they bring out any new color forms etc. Also looking forward to spending some time with the new grandson!