A couple of ideas...and some links to help...
One thing: him throwing himself down in the cage is what bunny people like to call a Dead Bunny Flop. It actually is him being REALLY happy.
(You can read more about it
here. Also check out the thread on
Binkies and Bunny Flops in the
Bunny 101 thread in the
Lagomorph Library here in the forum.)
About the peeing: have you thought about just buying a kitty litterbox, and putting some wood pellet litter in it for him to pee in? If you cover it with a good helping of hay (which he should get an unlimited supply of anyway), he'll be drawn to going there for the bathroom. Not to mention, him having a litterbox will help him know where to "go" all the time...and will save pee from getting outside his cage.
(To help, check out the
Litter Training and
Litter and Litter Boxes sections in the
Bunny 101 thread in the
Lagomorph Library here in the forum.)
About him chewing paper while you're trying to throw it away: it sounds like he might have been trying to play with you. One of the things bunnies like is to play "toss". Some bunnies will even go fetch it and bring it back!
Another thing it might be, and something I've found in my own rabbits: it could be that he prefers the "shreddies" to stay. My Maisie gets really stressed when I change her cage too much, and gets so much in the way while I'm trying to clean her cage, I finally just decided to put her in a carrier while I go about my business. It might be him asking for his shreddies to stay. You can put him in a nice sized carrier while you clean his cage. Just be sure he has hay, water, and maybe a favorite toy to keep him company.
You can let him out to exercise, but just watch him if he's not fully litter-trained, as he might have "accidents" while he's out. Just soak up the urine with a paper towel and put the paper towel in his box, and he'll start getting the idea that it's where he's supposed to "go". Another thing: putting the hay on top of his litter will promote him WANTING to go only there, as buns like to eat while "going". The hay acts as a kind of magazine. Hehe!
That's about all I can think of right now. Just be sure to take some time to do some reading in our
Lagomorph Library, as it has MANY MANY articles and LOADS of helpful information!
Here are some threads that might be worth reading to start off with:
Aggression
Books About Rabbits
Bunny Ideas and Accessories
Bunny Proofing Your House
Cages and Hutches: Housing your Rabbit
Feeding Your Rabbit
Finding A Vet
Glossary: Some Terms You'll See in the Rabbit World
Hay: All About it
Household Hazards
Lifting a Rabbit
NIC Cage Tutorial
Odor Control
Pellets
Poop!
The Rabbits Online Cheat Sheet
Toys!
Vegetables
Sorry, I know that's a lot...but as you can see, the Lagamorph Library has LOADS of helpful information, and is worth checking out!
Keep us updated, ok?
Hugs!
Rosie*