Familiar
They are known as a Familiar.
A cat. Usual a black one known as a familiar
Usually they are simply a pet. However, my first cat came to me at the same time I began studying witch craft (I've always been a spell caster and witch but I began studying the history and practices of other witches a few years ago) because of this I refer to her as my familiar. Usually a familiar is an animal that holds a special place in a witches life and craft.
When we lose an animal helper, (familiar) as happens in life... these animals are not supernatural and do not live forever, we mourn them, in whatever manner our personal path (and heart) dictates then go on with our lives, most often, if we need an animal helper, the gods will provide.
Witches do not perform experiments. They perform spells and rituals similar to what other religions perform. As far as the correlation between cats and witches goes. Most Witches (or Wiccans or member of any other Pagan sect) are worshipers of nature. Most witches have what is called a Familiar. A familiar is an animal that a person chooses as their pet. Sometimes they are considered their spirit animal. Not all "Witches" are cat people. Some like other animals like dogs or really any other animal that is tame and could be considered a pet. Cats are an extremely mysterious creature. Cat's already have a lot of superstitious ideas laid upon them so when you add that to the reputations of Witches or the Occult arts you basically get a heavy and very mysterious vibe to Pagan practitioners.
Witches do not exist and hence i cannot think of any animal which would do so.
penfold (danger mouse's sidekick) is a hamster
It depends on what branch of paganism you look at. The goddess Bast is often symbolized by a black cat. They are also well known as witches familiars, though any animal can be a familiar.
a mouse
The witches hat is at Graices or Able sisters. Check.
bird
cats