When it comes to large carp appearing bloated, it's often a question of genetics rather than being overfed and obese. In the never ending drive to achieve greater weights, fish breeders often chase "ideals" that don't necessarily coincide wth those of a fair number of anglers. If carp sizes (and body shapes) had been left entirely to nature, I suspect that carp would rarely exceed 40lb in the UK. It's possible that the figure might be much less.
I suspect that an awful lot of the more outlandishly shaped carp are nothing more that genetic deformities. Snub noses, weird shaped heads, oddly positioned and sized mouths are all fairly commonly seen, especially in commercial venues.
When it comes to colouration of fish, genetics also play a part, but the most significant factors seem to be water quality, water clarity and diet. The most beautifully coloured fish I've ever encountered have invariably come from clear water venues.
The strangest variations in fish colouration I've seen are on waters that vary in clarity. The Dales rivers can run like tap water at times, but they often run the colour of stewed tea for long periods. The fish often seem to vary in how vivid they are depending on the water colour.
The most obvious genetic variations I've encountered have been in barbel. In some of the rivers I frequent, the are long, lean, and quite pale barbel alongside shorter, stockier, and more golden/brassy fish. The speculation on this is that the long, lean, fish might be a native strain and the shorter, stockier, fish be those that have origins in the EA stock fish which would have links to Trent fish.