1.5 gallons will be ok but
ONLY if you keep up on water matience. I would suggest 2 water changes a week. One should be a 100% where you clean out the gravel to get any uneatten food and poop out of there so it won;t pollute the water. The other water change should be a 50% where you just change out the water. If you remove him, be sure to slowly acclimate him back into the water. If he is just plopped back in there and the water is too hot/cold from what he is used to, he can go into shock :( Some people may suggest 3 water changes. IMO - that's a bit excessive. It doubt it would hurt though. If you can get a bigger home for him, that would be wonderful but I know alot of people don't have room or funds to do bigger tanks. However if you really want to give him more swimming space and funds are low - those clear plastic storage bins walmart sells work great

I've used them and then just upgraded to a real tank when I had the funds to do so.
Why did the friend suggest a fungus? Does he have white fuzzy patches on him which would indicate a fungus?
his problem may be simply that he is too cold. Bettas are tropical fish and should have water temps between 76-82. If he does not have a heater, that should be one of the first things you get when funds become avalible. Ebay or Amazon may be cheaper then an actual petstore.
Sometimes it takes a few days for them to warm up to their new home and some bettas won't eat for a few days. Are there any places for him to hide in and explore in his tank?
Any other physical symptoms - like white dots, fuzzies, stringy white poo..anything like that? rapid gill movement?
you might want to cover the bowl, some bettas will jump put of them. If you have saran wrap, that would work but be sure to poke holes in the top so he can get some air in there.