Thunder - Anistark gave you some great advice. I was going to post about limiting your bunny's time out too.
Edited to add a "TOY" section
Regarding the litter. The compressed pine sawdust is fine. It's really the only time pine is okay because the toxic oils are dried out. Some bunnies may find the pine smell too strong and stay away. Though that didn't happen with mine, when I did use pine woodstove pellets (same as the cat litter "felinepine' but so much cheaper when bought at a hardware store)
Let us know how long the lavender oil works. If it seems to deter for more than a few days, I'll add that to my home-proofing tips (I'll add Tip from member:Thunder)
It is very normal for a bunny to hang out in his litterbox. Some bunnies do it because they feel safer there since they have thoroughly marked it and claimed it as theirs. Their poop has messages in it, and of course though we humans aren't going to "read it", a bunny has basically said what their sex is, how old they are, how dominant they are, if they are ready for nooky, or they want to be left alone. And so they "send" out the message and feel they have done their part., and then they can relax more.
IF he ends up making it his bed, and pooing some place else, you may need to get another box.
Again, don't be discouraged if he doesn't get this all right away, he is reaching sexual maturity, and so don't be surprised if he gets even more wacky, he might even start to become territorial of his "space" and can growl and grunt as his hormones surge.
Neutering: Usually when his testicles drop which is around 4 months. He will become EXTREMELY friendly soon, and it will become obvious. He'll start circling you, and if you listen very carefully, you'll hear a low honk noise, and then your leg or arm may be assaulted by bunny love. You can offer a stuff sock.
It would be a good idea to find a rabbit savvy vet? Do you have one? IF not, I can offer some info on how to find one. It is extremely important that the vet has rabbit experience, as the surgery requires some special expertise - not the same as cat and dogs.
Toys - The more his hormones surge, the more destructive he may become. So here are some more ideas:
You can turn an ordinary cardboard roll into something a little more exciting. Stuff it with hay, and bury a couple of raisins or some other treat inside. Then punch/cut a few holes throughout the roll so he can get a better whiff of the treat inside, and it helps give him a chewing point to start with.
You can do the same thing with a small lunch paper bag. I put a few of those around the house.
Soak Popsicle sticks in apple juice. I usually weave the sticks in the bars their pen.
Oh, and phonebooks, big 'ol phonebooks. Many bunnies love to tear those up. Check out the "video section" of this site. (In the Gallery)