Well in regards of litter odour I use a very effective powder with scent and baking soda from Arm and hammer. You'll find it in the litter shelves at the grocery store.
I see where you come from. You don't want to be noticed by litter and be able to keep your kitty cat without any problems.
I've never tried toilet training but yes, what people say here it's true, they can fall inside.
My parents had a small cat she naturally used to go to the toilet to pee. No one ever taught her or even tried to toilet train her at all. One of those curious cases.
Anyways I've seen products that offer to help you to toilet train your cat (I've never tried them) I remember one called "Litter Kwitter" I think. Who knows, if you really need her to go in the toilet perhaps you could give this a try.
" How we behave toward cats here below determines our status in heaven."
- Robert A. Heinlein