Rabbits do clean themselves, just like cat. They're quite clean actually.
I've had about 5 different rabbits as pets and I've found that it is so much easier to clean their cages out if you train the rabbit to use a litter box. It's not too difficult to teach them. Whenever they poop or pee anywhere, just move it to the litter box and the rabbit will soon get the hint that that is where it should go. Rabbits are pretty clean and you'll find that they like to keep all their waste in one spot. That's why the litter box is so awesome. Plus you just really have to worry about cleaning it out everyday.
As for the actual cage, I'd clean it every week because rabbits tend to shed or get food all over the place. Normal animal stuff. Really the best way to decide if it's time to clean the cage is if it looks dirty. Pretty simple huh?
They need to be let out of their cage regularly to stretch out their legs and to just run around. Leaving them in the cage will cause them to get over weight and can cause the rabbit inflammation to their feet for sitting on them all the time. In our own home we'd allow our rabbits to run around the house and then just put them in the cage when it was time for all of us to go to bed. Always make sure the litter box is reachable for the rabbit or you'll find pellets under your bed and behind the furniture. Trust me, their urine is not pretty smelling AT ALL.
As for food, hay generally works. Along with hay, greens are a vital part of the rabbits diet because they will provide all of the nutrients that hay provides, but in addition fresh greens will provide the rabbit with water. Yes, the rabbit will have permanent access to fresh drinking water, but you can't force the rabbit to drink. When the rabbit consumes greens they are also getting a sure supply of water. Good options are broccoli, cabbage, celery, and most of the greens that are dark in color. Occasionally feed your rabbit fruits such as pineapple, pear, peach, papaya, and any of the sweet berries. It's a real treat for them.
I think that you'll find that your rabbit has a personality of it's own and if you really watch it and get to know it's characteristics, it'll tell you when it's hungry or when it's irritated that it's cage is a mess. They're quite outgoing little boogers when they're so completely comfortable.
But yes, if you have any other questions just feel free to ask!
