If we get a new kitten..

..how likely is it that we won't be able to train him/her to scratch only the cat tree? What about improper urination? Will he mimic the bad behavior of one of my cats?

Just a few short questions. What do you think?

If you don't have experience with a cat, those questions can be very difficult to answer. A cat will scratch. It's not to sharpen his claws, as some think, although one effect is to pull the old sheaths off claws, leaving new, sharp ones. Some cats scratch on lots of things. Some stick to the supplied cat tree, or whatever. You can keep his claws trimmed, which helps some.

If you put the kitten in a small room with a litter box (low-sided, like a cake pan, if the kitten is small), most kittens will use a litter box with no problems. If you are careful to get it spayed or neutered well before puberty (by about 4 months of age), a lot of the later problems can be avoided.

I have 4 cats and not 1 scratches on the furniture so I gotta believe its learned behavior. I just got lucky. The first one never did and the rest followed suit.