My suggestions for your new kitty is to keep her isolated in a separate room
for a while....A 'cage is really no help for a cat, they just want out!

Unfortunately, Nellie newbie - the 5 year old adult female - doesn't appear to
use a litterbox. I have her isolated in my bedroom. She peed on my bed for 2
nights (using the litterbox for peeing the first night only. After that, she
hasn't used it.) She deficated on my quilt on the 3rd night.

I realize that she has a high level of stress: being taken from her home, put
into a shelter for a month, coming to a new home w/a cat, having that cat jump
on her several times..being shuttled to the vet for 3 days for exam & dental
cleaning (she wasn't keeping food down..she's received a clean bill of health,
though). I spend time with her in the bedroom (even though my other cat is
crying on the other side of the door). What can I do to teach her to use the
box?