Well, to answer your second question, rabbits mostly act like rabbits. I’d say that they have some “dog-like” things they do and some “cat-like” things, and the proportion for each is different from bunny to bunny. Like, Humphrey is like a big floppy kitty a lot of the time– he’s lazy and flops under things and is demanding when it comes to attention and food when *he* wants it, but he’s also more loyal and cuddly and gets lonely more easily than Monty does, so in those ways I’d say he’s more like a dog. Rabbits mostly act like rabbits, but lots of them do cat or dog “things.”
Your first question is in some ways a little easier to answer (generally speaking, rabbits and cats are a safer combination than rabbits and dogs), but also has a lot to do with the tempermant of each specific animal. Some “solitary” rabbits who don’t get along with other bunnies get along very well with cats, who are usually not terribly interested in chasing rabbits. Lots of people have homes where cats and rabbits live happily in peace, but you do have to know the temperment of your cat (does she scratch things with little provocation? is she much, much bigger than your bunny?) as well as of your bunny (an aggressive rabbit may eventually provoke an otherwise laid-back cat into attacking). When introducing a rabbit and a cat together, the upmost caution should be taken and they should be watched very carefully, and many of their subsequent meetings should also be monitored. However, cats may eventually be left more or less alone with rabbits without much worry.
Dogs on the other hand have a natural instinct to chase and bite rabbit-sized fuzzy things– in fact, many breeds of og were originally created solely to chase bunnies. This doesn’t mean that your dog and your rabbit can *never* be friends, but it does mean that you can never leave your dog alone with your rabbit even if he’s completely “trustworthy.” There are too many horror stories of the dog suddenly “snapping” when the owner leaves, or even of them accidentally stepping on the poor bunny. Dogs may think they’re playing when they pick Fluffy up and carry him around, but the rabbit thinks he’s being eaten and may go into shock or, more simply, may have been hurt/crushed/etc when the dog took him in their mouth. Any intorduction between a dog and a rabbit should first occur through a fence, and when sufficent trust is established, with the dog on a short leash and someone ready to pick up the bunny if he’s in danger.
Cats tend to be safer companions for rabbits, but here’s a great article on how dog/rabbit bonding *can* work out when supervised:
http://www.rabbitnetwork.org/articles/dogs.shtml
I can’t currently find the links for steps to ensure happy and safe cat/rabbit and dog/rabbit bonding, but I’ll post those too if I stumble across them.