Hi bella, Since fasting is mildly dehydrating I would recommend that if you are going to take a bath while fasting that you bathe quickly and get out of the water. I would never recommend that anyone take a detox bath with Epsom Salt while fasting.
I would never swim in a chlorinated pool even if I was not fasting. It sounds like you already know that chlorine is a carcinogen. (Iodine is displaced by chlorine in the body.)
I would not recommend putting salt in your water. I am assuming you are referring to Celtic Sea Salt ; it contains minerals. I know there are many different variations of fasting, but a Water Fast is fasting on water only.
Some people do clear water enemas the first few days of fasting to relieve detox symptoms or as needed. I do not.