I have some advice.. I hope others can help out as well..
Chins basically poop anywhere when they feel the need. At least mine do. I have heard of litter training, but never seen it.
They should be kept in cooler, less humid rooms since their dense fur is plenty warm.
As far as the biting goes, that will take time. When she bites, blow lightly on her nose, so then she will associate that discomfort whenever shes being bad. Otherwise, continue to have playtimes with her and let her come to you instead of grabbing/picking her up. She will eventually get use to you.