35C is way too hot for a GTP, especially a baby. They need a steady temp of about 28-29C as small juvies, and because they need to be kept in small tubs for the first few months, a gradient is hard to arrange, hence the conservative but steady temp. A young GTP would dehydrate very quickly at 35C, and a high temp like that would significantly affect the interest in food.
Baby GTPs DO drink from water bowls, just as adults do, as well as drinking droplets from their skin. A captive bred hatchy fed thawed or even fresh killed pink mice has nil chance of worms, but may pick up protozoan parasites if the rodents aren't from clean stock, or if it is kept in unclean conditions. The black or dark patch on the belly is bile staining from the gall bladder, and this can appear within a couple of hours of death especially if the enclosure is too hot.
The animal looks very small and was probably not well enough established to go to a novice. I don't sell mine unless I'm assured that the buyer knows what they're doing, and I'm sure that the animals are established enough to feed readily for their new owners. This usually means a minimum of 12-15 feeds during the time I have them.
Jamie.