Why is my Betta fish suddenly so different/sick? What can I do?

I’ll start from the beginning. I bought a bluish purple betta fish on monday. He was slightly thin and uncolorful, but so were all the others. I bought one who looked healthy, no scum, good swimming, good scales, etc. Tuesday, he just looked better and better. His fins were unfurling and his color was brightening. He was swimming around happily. He ate all I gave him quickly. He would interact with me, and follow my finger. Wednesday, He seemed to be doing fine. His color started fading though. He still interacted with me. Thursday, I wasn’t home most of the day. I fed him though. He discovered his cave. Friday he looked terrible. He never never never came out of his cave and he wouldn’t eat. His head was losing color. Little worse Saturday. Sunday, today, he looks TERRIBLE and I’m so depressed! His whole body except for the fins is a brownish greyish color, his gills puff way out, he won’t eat, and he hardly comes out of his cave!!! I just changed the water and cleaned the pebbles, cave/plant, and bowl.

A little information on how I am treating him. Zeta Pi is kept in a little over a gallon bowl. His water comes from our sink and is treated with Stress Coat+. We sort of live in the country so the water is NOT city water. His habitat includes some pebbles, a cave with a few fake plants attached to it, and he is kept in a shelf where three sides of his bowl have white wall beside them. He’s in my room, which is not a terribly busy room. A pretty stress free spot, I think. His water thermometer says it’s just at 60 degrees Fahrenheit. I think it’s too cold but the lady at the pet store said it’s fine. I have found tiny thin curled brown things at the bottom of his bowl every two days or so, but I thought they were just poop. And I feed him Betta Bites, three in the morning and three at night, like the label said for me to do. He never eats anymore.

WHAT am I doing WRONG? I thought they were fairly easy to care for! I had done hours and hours of research before I bought him! Why is he like this? Is he really sick? Is he going to die? My main concern is that his water is too cold. My pet store doesn’t sell heaters for bowls, and they said I didn’t need one! Should I buy one off the internet? Where can I find one and what brand is best? Please help, experienced Betta owners!