For the first question, do you mean she goes elsewhere? If she isn't pooping at all, it could be a medical problem as well as if she's going in more places other than the litter box. Since she's still urinating in the litter box, she's obviously litter trained. She also must not be completely afraid of the litter box since she's still using it. I, personally, would bring this up to a vet.
The second question is nothing to worry about. Your cat is attempting to bury her food to save it for later, or bury her fecal matter/urine to hide the scent from predators. It's in their instinct from their ancestors living in the wild; bury things to save, or hide the scent, so that no predators can find it later. As long as she isn't clawing the carpet or anything that personally bothers you, it's fine. Just keep everything around the food bowl clear so she doesn't drag anything into it, especially if you feed her wet food.