I can't speak on all of these, but I myself am a trans guy so I may be able to help with that!
When it comes to writing trans characters—really, this can apply to characters of any marginalized group—the biggest advice I have is to not make their transness into a personality trait. Someone I saw in a thread here around a year ago put it really well: you should be able to describe the character and get a really good grasp of who they are as a person without needing to mention that they are trans/queer/another marginalized identity. Being trans is sure to be an integral part of someone's identity and likely shaped a lot of their life experiences, and it's impossible to completely separate that from who they are as a person—I would not be the person I am today if I were cisgender, that's for sure. But the idea is that them being transgender is not being used as a replacement for an actual, fleshed-out personality, and you can explain who they are without mentioning it. Just like if you had a transgender friend and you were asked to describe their personality to someone who didn't know them, you would, you know, describe their personality, and very likely not say that they were trans—it would be a strange and irrelevant comment! I had some difficultly wording this, but I hope you understand what I'm trying to get across.
As for things more specific to trans men, I'll assume you know some basics of transitioning such as taking testosterone or getting top surgery. The internet is a great resource for medical information on HRT, different types of gender-affirming surgery a trans man might get, etc. What's important to remember is that everyone's transition is different, and many trans people decide not to medically transition at all. The world that your story takes place in may be different, but it's also worth mentioning that in the real world, even in places where it's legal, transgender healthcare is incredibly difficult to get. Many trans people would like to transition but are unable to because of the lack of resources.
One last specific thing that I see sometimes in writing and that always bothers me—it is super difficult and dangerous to fight or do any sort of strenuous physical activity while wearing a chest binder (exactly what it sounds like, it's an undergarment for people that have not gotten top surgery that binds the chest and flattens it), except maybe in cases where the character is wearing a size up, but even then, it's a bit of a stretch. Even wearing a binder for too long can be dangerous, and a character wearing one will probably get out of breath easily, even if they're very physically fit. Binders are not the only option for people who do not have/want top surgery, but they're one of the most popular, so they're worth doing some research into!
I was also going to talk about my experience living in a small city, but for some reason it was much more difficult for me to gather my thoughts on that, so I may come around later and give some advice on it. If you have any more specific questions on anything, let me know and I'll answer them to the best of my ability :)