Hi ~ worry not, i also went through an obession with my cat's poo
She sounds so lucky to have you and how great she wants to stop inside nice and snuggly instead of out in the elements.
Did the Vet check for a microchip? Hopefully, a good vet maybe able to tell you her age and give her a good check over.
Yes kitten food is good for building her up, also try some mince and cheese if she'll eat it.
I'd try not to worry too much about the poo. When it's runny is there blood in it? Does she go alot, little and often? or about 1/2 a day?
Sorry for the questions but just trying to get a better picture
