1) Will they eventually kill each other?
They are living animals. No one can say with certainly what will happen. Whether they will get along or not depends on a lot of different things, their personality, how much room hey have, and things like that. The number of hens is not nearly as important as many people believe, but you are certainly OK in that aspect with 22. The more room they have the better so the loser can run away and just avoid the alpha rooster to start with.
What normally happens is that the two reach an accommodation, much like they had until recently. They work out how to keep the flock protected with both having a part. They may split the flock with each having his own harem. With 22 hens, don’t be surprised to see some hens split off without a rooster. I’ve had two roosters that hung out with each other more than with the hens. They still knew which was alpha and the hens were all fertilized. Either rooster could be the father, thou the second-in-command had to be a bit sneaky about that. When they split the flock into their own harem either rooster could still be the father of any chick. It’s possible one could kill the other, but from what I read in your post, it’s not likely.
2) Should I get rid of one rooster? Can two roosters get along?
See above.
3) Should I separate Big Jim (behind his comb there is a gash) until he is healed?
You could, but you have an option. Get blue kote or something similar and try that. It’s possible, not guaranteed but possible, the other chickens could see a raw sore and peck at it. Blue kote might disguise the wound so they don’t peck it. Or they might leave it alone anyway. But it could be possible your hens kill that rooster by pecking at the wound.
The problem with removing him for any length of time is that when you reintroduce him the two will probably fight again. That’s not that big a deal unless one gets hurt again. Usually they don’t get hurt when they fight but stuff happens.
I don’t know what I’d do in your case. Either one has risks but moist of the time either one will work. Maybe select the one where you can be around to see what happens?
4) Is this just a "springtime" thing?
Spring could easily be a factor. Longer days tend to wake up certain hormones in roosters. Part of it could be the maturity level of your roosters. Dominance is not all that much about size. It’s about the spirit in the chicken. It’s not that unusual for smaller chickens to be dominant. Maturity plays a part too. It could easily be that your smaller chicken was slower to mature and is just now coming into full maturity. That can happen in the pecking order with your hens too. As they mature at different rates the pecking order can change.
Multiple roosters can easily coexist in a flock. Many of us have that. But I always recommend you keep as few roosters as you can and still meet your goals. It’s not that you are guaranteed to have problems with more roosters, just that you have a little more chance of problems. But with what I envision with your set-up and room, two should be able to coexist.
