first off welcome to the forum. Second, the white marks are normal. They are individual to each frog, kinda like freckles. If your vet is suggesting barrio treatment for these spots-- get a differnent vet. Third, I don't think you'd need heat at all, but since you have it already. ....
Fourth, tank size.. It says two adult reds can be in a 10 gal tank. So that's 5 gal a frog.
All the moving will stress them out, calm down, leave them where they are and let them settle in. It takes up to two months for them to really sit and be happy. Your night light is really for you're viewing, you can shut it off when you go to bed. Reds can get down to 60 I think before you have to worry. My frogs get freiked out by the light so I don't use it. If they are hunting and moving around then they're fine with it.
As far as parisites, if he's not framiliar with red eyes, he's not framiliar with frogs at all. Get fecals done by someone else, and parisites are kinda normal, but take over when a frog is stressed.
Good luck, we'll see if there's anymore advise from other members.