Another sweater here, at least whilst training! When I was in Japan training in 38 degrees with no aircon, sweating was a matter of course for everyone, carry the face cloth in your jacket, wipe your wrists when necessary, shower after keiko.
I'm now back in the UK, and despite the climate change, I'm still sweating when I train. It's a natural reaction, and also a healthy one. When you're exposed to heat, exercising strenuously, you may lose several quarts of fluid in perspiration. A pea-sized bead of sweat can cool nearly one liter (about 1 quart) of blood 1 F.
As for athletes foot, I was unfortunate to cop a dose when I was in Japan. It didn't hurt, didn't itch, didn't stop me training (wore tabi to cover the foot), went to the doc's. As soon as I mentioned Aikido, the doc just smiled and said that it was probably the most common ailment amongst budoka in Japan, gave me a botle of liquid to treat it and it was gone in a little over two weeks. Not seen it since.