Cats don't know that it is bad to go outside the litter box. Cats use litter boxes because they want to; not because they've been trained to use them. Humans generally consider it a bad thing when their cats decide to urinate (or defecate) somewhere in the house that isn't in the litter box. This page gives some reasons for this problem and some possible solutions.
Scratching is a normal marking behavior in cats. They scratch things that are important to them - that are a prominent part of their home and territory.
To prevent them from damaging things that are important to you, you can:
Put scratching posts in prominent locations.
Try a variety of scratching posts to find your cat's preference.
Use Feliway and Feliscratch to discourage scratching on some things and to encourage it on others.
Trim their nails.
Apply nail caps such as Soft Paws.
Make the surfaces less desirable with foil or tape.
Human Directed Aggression
Human directed aggression is one of the few conditions in cats that is potentially life threatening to the people. A single cat scratch can lead to cat scratch disease which can be fatal in some individuals. A single cat bite, if not treated rapidly and effectively, can result in a bacterial septicemia in humans that can lead to rapid deterioration. If you do ever get bitten by a cat, call your doctor without delay.
When discussing the treatment of cat to human aggression, it is important to know that, as with all medicine, there are no guarantees. If you are living with a known aggressive cat, regardless of the treatment, you are at risk.
There are different forms of aggression in cats and it is important to differentiate between them when deciding on a treatment plan. They include play, status, petting induced, fear, and redirected aggression. A cat can have more than one of these. In addition to behavior modification, prescription drugs are often needed to resolve human directed aggression in cats.