I only use all natural/organic products. So no I don't use peroxide and haven't in years. I honestly can't remember if I used it while I had peeling lips or not. If I did it wasn't that often. And I don't bleach them either. I just floss a couple times a day and use this natural toothpaste made by Jason. I don't use mouthwash either.
Nope I only use the Avalon organics lip balm, nothing else touches my lips.
As far as supplements, I don't believe in those. I believe you can get everything you need naturally from the world. Plus supplements are just dried proteins or whatever, and I personally don't like to put anything dried into my body. I do, however, eat raw eggs, drink raw milk/cream/butter. I eat a lot of grass-fed beef and organic chicken. Whole milk yogurt, and nothing processed or anything.