every bunny is different and some take longer to bond to their human(s) than others. neutering might help since he's in the middle of the "teenage phase", but then again it might not... since you say you don't have plans to get him neutered in the near future, you may have to get used to him as-is for a while (I've heard they usually settle back down a bit after they're around a year old).
definitely spend as much time as you can in the same general area as your bunny - sit in the middle of the room watching TV, reading a book, doing work of some sort, etc. and just let him come up to you/scamper off as he pleases. my girls are definitely most interested in being near me when I'm in the middle of a craft project, lol. you've just gotta be patient and keep trying - while some bunnies do bond to their owner in a matter of days, others can take months to do so.
as far as picking him up for nail trimmings, bribery is a good way to train him. work with him just a little bit each day using a favorite treat (fruit works great, just remember they shouldn't have more than 1 tsp per 2 lbs body weight per day - split the fruit up into tiny pieces so you can get the most out of his daily allotment).
start by picking him up and sitting on the floor with him in your lap. as soon as you pick him up, give him a little treat. just hold him for maybe 15 seconds each time at first, then work up to 30, then 45, etc. until you can hold him for a couple minutes (you can also offer him a tiny treat when you put him back down). once you can hold him for a little while, flip him over, give him a tiny treat and set him upright again immediately. gradually build up the amount of time you keep him on his back, and as he learns to be comfortable with it, start playing with his cute little feet as you hold him (again, you can give another treat after you flip him upright again).
basically, you're teaching him that it's worth tolerating something he doesn't want you doing in order to get yummy treats.
when you go to clip his nails, keep a little pile of treats beside you (I like to use raisins or craisins so I don't really get my hands sticky... and so that they're in a box or bag where I can tuck them away from the loose bunny while I clip the captive one's nals
). I give one treat when I pick them up/flip them over, another treat every 1-2 paws depending on how feisty the bunny is that day, and one more when done. it generally takes me 3-5 raisins/craisins to get through nail trimming.
when trimming, be confident and quick as they can sense anxiety. rather than taking the time to precisely calculate where you want to cut, just err on the side of cutting too little off (since you can always go back for a little more) - snip the very tip and keep going, then double back to get any nails that are still a little too long. the faster you can get through each paw, the less squirmy the rabbit will be by the time you're done.
if nail trimming is really problematic, you can wrap him in a towel (aka "bunny burrito"), taking out one paw at a time to clip, or you can get someone else to hold him for you while you clip.