Sounds like he's coming around both with settling in and in starting to heal.
Each horse is different - but yes - even little stallions need to have politeness and manners. I have always followed the 3 second rule - he's really "naughty" or not following your rules, he gets "killed" for 3 seconds. Then I turn around and go on with whatever we were or are working on. I've learned that show ring training doesn't necessarily politeness/manners make. In fact, in too many cases, to me it seems like the manners aren't there at all and aren't even "known"!
Handle/school him the same way you do your mares. If he's rearing for hoof trimming, correct him and train him to stand and hold his hooves properly. If he's rearing for the fronts, I suspect he's not any better for his rear - just train him.
Our first stallion was a riding pony. He learned from the 1st week that I owned him, that when he was in "work mode", he was to ignore the girls - even if they ran up to him backwards and stuck their tails in his face! Years later, even after he'd gone to just a pasture breeding "pet" (the girls' had all outgrown him for riding, he wasn't being used for riding lessons, driving or regular pony rides), you could pull him out and work with him as long as you weren't using his "breeding chain" (see pp below). During his "work years" - he was a riding pony for 2 of our 3 daughters and went out on combined sex trail rides. Often he was the best mannered horse on the ride!! He was also used for 3 years for beginner riding lessons at a local barn - though usually he was the only one in the ring at the time depending on the level the kids were at. A good mind, consistent handling and work are what worked for him.
When you go to breed him - be consistent. I'd recommend developing a certain spot that you always go to to wash both of your horses and also use only one specific halter for breeding (for him). I didn't always have an extra halter for my breeding stallions - but they learned that if I brought out a certain chain (that I ran thru the halter rings and thru their mouths) - that it was breeding time. It gets to the point they get excited and "ready" when they see the chain coming - making it easier to wash and prepare them.
Our 2nd stallion took longer. He was a tough one to get settled. Our vet didn't recommend sedating him - but letting him run himself - and run he did. He refused to eat - and I spent many days, weeks - even months with him while he "stood" (constantly moving) tied and hand fed him. I despaired of ever having him "be a horse" - he was constantly screaming, constantly moving, pawing, rearing - even when tied or cross tied. I'm not sure when he finally started to settle. He'd been shown, he'd been started driving (I was a green driver and I sure wasn't going to try working him that way!!) and he was a blithering idiot when he arrived at our farm. I went to TX to pick him up and he was great - to load, to unload and play with at several places with my Dad (living in a special needs home) and haul home until we got to the farm with mares and ANOTHER STALLION... I even called the previous owner and asked what feed/hay she'd used for him and had it ordered in JUST FOR HIM to try to get him to eat. He went from beautifully round to a lean, mean running machine that was actually way too light and boney. To top it off, getting him to breed a mare was almost impossible - he was a shy breeder that was more concerned with everything else. None of the mares that I bred him to that first year settled (most of his semen ended up on the ground!). I decided to give him another year - to settle in, to learn the manners I was struggling to teach him (they don't learn if you can't even get their attention and he didn't give it easily). The 2nd year, he appeared to settle the one mare that I bred him to... But it was work to get her bred, let me tell you.
He and our original stallion got to the point where they "postured" and "played" running the fence lines off and on all day. They'd holler at each other, drive and herd "their mares", mark piles of manure at each end of their run. Never did get any real good pictures of either of them then - wish I had. Sometimes, much later, I would let one or the other into a pasture that put them next to each other - making sure that the fence was secure and that it was HOT. He finally seemed to accept that he was staying, that he had his own group of mares that weren't going to "the other one" and the manners finally started "sticking". I want to say it was the 3rd year before this occurred - so it took 2 solid years of dealing with his "crap". I am now ground driving him with one of the mares he's sired 3 foals with. They will work as a pair until I find a better match for either of them... Like our original stallion, he now understands and accepts that there is a "work mode", BUT it took years of work to get him to this point. It was a shocking surprise after handling him for a week with no other ponies/horses around. I wasn't prepared for the change in his personality and attitude.
As a teenager and as a young adult, I worked for several farms and ranches that had multiple stallions and never had what he became for a while. While he was only the 4th stallion I'd personally handled (2nd Shetland) on our farm, I didn't consider myself a complete beginner. He left me stunned and humbled! And then the work began to "bring him around". I'm glad that I gave him the chance! He's siring some really nice babies for us and is back to that original "nice" behavior he had when I first handled him, it took work to get there. In other situations and with some other people I know - he'd have either ended up dead, sold to some other
"poor soul" or gelded... Not sure that gelding would have worked with him at first, personally I don't think it would have made a difference right away.
Good luck with your boy.