Yo, Johnny, I didn’t get the handle “Broomstick” because I fly airplanes… (yes, it’s TRUE! Some witches DO fly… but nowadays we use aircraft. Brooms can give you splinters in places you don’t want to know about!)
I think you have a good grip on some basics, but any question like “what do witches believe?” is a real minefield. There’s not a an official Book of Dogma like the monotheisms have. Practices range all over the place. Since tolerance is considered a virture there is a really wide range of acceptable practices in the larger Neo-Pagan community.
I tend to think spellwork and prayer are equivalent on many (although not all) levels, so it’s a good comparison for someone just starting to study witchcraft whose background is Judeo-Christian. If you want something more detailed about my personal practices/beliefs e-mail me.