I think the red one will be OK. Clean, warm water and good nutrition should clear up both the red area around the gills and his buoyancy issues.
What type of food do you have? On this forum, New Life Spectrum (NLS) Betta pellets and Omega One Betta Buffet are the two most often recommended foods. Both have quality proteins, without lots of fillers/grains. (Fillers and grains such as wheat, corn, soybean, gluten, etc. are often found in lower quality foods, and can cause constipation and bloating in sensitive bettas.)
I can't really see the blue on well in the photos. How far down does the fin rot go? How far is it from his body?