They will adapt in time.
Cat carrier for her trips is a must.
Stray....have her tested for feline leukemia etc...
Shots are a must.
If a cat .... Any cat ever bites you and breaks the skin see a doctor. Not a few days later but right away. Cats carry a bacteria that can kill if it gets in the bloodstream. For real, not kidding.
A good scratching post is a must. Easy to make with a bit of low pile carpet, 2x4 and a chunk of plywood for the base. Ours was built with an air stapler and screws but I am sure there are other ways to attach the carpet. Just 2.5' tall is tall enough for scratching on.
A cat tower can be easily built with some sonotube, 4x4, carpet and sisal rope. Attach everything to a base of plywood so it does not tip over.
Cats like to be up high and that tower will help give her a dog free zone. It will also help keep her off any bookshelves.
Having her spayed will help keep her from feeling the need to run off as well as prevent health issues. I am pro-spay and neuter.
Catnip and kitty toys are good things to have too. If your dog might swallow a kitty toy I suggest the ones that are a stick, string and toy on the end. It puts YOU in control of where the toys are. A bit of catnip rubbed into the scratching post and tower will draw her to them....and save your furniture.
I would not ever declaw a cat. The procedure basically cuts off the equivalent of the last joint on a hand. It can make scratching in litter painful......causing her to potty everywhere else.

That is a smell that does not wash out.
Enjoy her, pet her, love her and play with her.
Oh and kitties are self washing.
