I apologize if any of this is stuff you already know or have tried!
The first thing, is it sounds to me like your bun is physically uncomfortable and under stimulated. Yes, neutering will help with some behaviors, but not all. The good news is some or all of these behavior issues might be his habitat and therefore easily fixed! You mentioned he's in a cage/pen. If that cage (no matter how big it is) is his only personal space, he almost certainly feels cramped and territorial, which might be contributing to his bathroom problem. Additionally, (I'm sure you know this, but I'm obligated to say) cages are really hard on bunny paws and physically painful to them. Regardless of whether rabbits have carpet or bedding, they're going to dig at their ground because that's what they do, but if you line his space with 1' carpet squares he can hop comfortably, and you can throw them out once he's destroyed them. Personally, I bought a carpet that I know mine would destroy with digging and I have to buy a new one every 9 months. That's life!
I'm a musician and my apartment is covered in cables, wires, and expensive instruments. It took literally hours to cover every cable is split loom tubing, and find a storage method for instruments, but it's worth it because now my bun can hop around, explore, and run off her excess energy. You can buy this stuff online or in any hardware store for dirt cheap. It'll mean your bun can blow off some steam (supervised, until he's committed to his litter box!) and you'll also be able to bond with him, which I'm sure you are both craving!
Regarding the litter box training, there are some really great youtube videos on the matter, as well as several threads on this forum- definitely check them out! Also, make sure his litter box is the right size. Esther is a digger, so her box has higher walls and is big enough for her to fully stretch out in- this really helps to contain more of her mess! I've also heard a lot of people buy fully covered litter boxes (like cats use) to fully contain any digging. By using a mix of paper bedding for the business half of the box, and hay in the other half of the box, she also has something to do while she's in there beside use the bathroom and dig. Distracting her with hay is the perfect answer. Try it out for your guy if you haven't yet! Also- wood pellets can be too hard and uncomfortable for more sensitive rabbits, leading them to dig around looking for more comfortable ground to sit on.
Another thing that makes me think he's physically uncomfortable and acting out is that you mentioned a water bottle. I totally understand the frustration of spilled water, but he's probably not getting enough water unless he has a bowl. A variety of sellers make great no-tip-over bowls, either with rubber bottoms, or combo water and food bowls that are stainless steel set into molded plastic. Something like this will remove both the rattling water bottle problem and the spilled water problem, and you can get either kind of bowl for about $10 with some sleuthing.
Last thing- the nipping. Esther is very communicative, but at first I thought she was just mean. She growls, she nips, and she needs a fair bit of alone time, which I thought meant she was rude and hated me BUT she is truly sweet, affectionate, intelligent, patient, and very loving. I just didn't speak Rabbit at first. The more one-on-one time you spend just watching your bun and sharing time with him the more you will learn his signals. Esther nips because she wants me to move, or because I'm too close to her very special spot on the carpet that's just for her, or most often because she's already tried to tell me something with her body language that I missed. When she nips or growls at me, she's shouting because I missed her signals the first three times that she is scared, or tired, or that petting time is over. Learn his signals and earn his trust. Rabbits notoriously do no respond well to punishment. Rewarding good behavior will get you further than punishing bad. You sound overwhelmed, but I promise you're going to fall in love with the little guy with some reevaluation, adjustments, and time!