The .25 of ammonia is hopefully closer to 0. Your test results do seem to show the tank is cycled. What test kit do you use to test your water?
Your tanks temperature is definitely a risk, and it will exasperate other issues as well as causing stress, plus if you had a heat wave you have no room for error, the temp could rise over 24 degrees Celsius which could be fatal if left for too long. There will be no simple efficient method of dropping your tanks temperature from 22 degrees Celsius to 16-18 other than purchasing a chiller. You can try placing fans blowing on the surface of the water and make sure you have a lid which can allow evaporation, then see how low that drops your temperature, but I doubt it will be significant.
Your Axolotl does seem like it could be slightly bloated, its hard to tell in those images so upload some more, slightly further away at various angles.
Red skin is usually attributed to ammonia burn (poor water quality), but since your tank appears to be cycled and the gills are in good condition I'm not sure if that is the issue.
You'd do best to find a vet near by that can deal with amphibians just in case, better to be safe than sorry.