I have 4 rabbits and 2 cats and never the twain shall meet! The buns are outdoors in enclosures designed to keep foxes out so they obviously also keep cats out! At my previous house we used to let the rabbits run round the garden and they did scare cats off, but my two cats now are clearly inherent hunters so I wouldn't risk it.
I guess there's no reason why you can't have cats and rabbits, I think you will have to start on the premise that they will need to be entirely separate and safe (including making sure the rabbits feel safe even in their enclosure), and if the cat is clearly ok with them, then that would be a bonus.
In answer to your other questions - cats can be quite destructive, equally they can be totally ordered. It's all down to the individual personality again, some like to sharpen their claws on your furniture/stairs and some are happy with a scratching post or tree in the garden. It's one of the reasons I prefer slightly older cats - usually more relaxed and less likely to trash your house!
Also having your own can stop stray cats coming into your garden but again it depends on the individuals involved - if your cat is a particularly submissive one, it won't stop them, but if yours is territorial it may well do.