Testosterone

Yes, your Adam's apple will grow. However this depends on genetics. Some men just don't have really protruding ones.

From watching many transition videos on YouTube, it seems that the average is around 2-3 weeks for beginning to sound like a cis guy. You'll have a young, 16 year old boy kind of voice until you reach almost a year, and by then it will be pretty much fully matured. But again, this depends on the person and how the voice sounded to begin with.

Every guy gets more body hair, but how much depends on genetics. Luckily my dad doesn't have a case of hard to shave carpet-chest.

Height most likely will not change, depending on how young you start. Some changes in soft tissue and muscle and such may make you appear slightly taller.

Age limit depends on the state

It does mean physically. Someone who starts as a teenager is stopping any extra transformation estrogen would have brought. If their growth plates aren't fused, they may grow in height as well. Someone who is older, estrogen has taken it's full toll.
This is more obvious in trans woman than trans men, as ladies who waited too long already have deep voices and such from the testosterone they produced in puberty.

A guy I used to know said that he became less emotional. Less able to cry, less mood swings, and such. Many other trans guys online have also said that.
He also said, since he is happier in his body now, he has become more confident and less depressed. But that should be obvious.

 

- A more prominent adam's apple will vary on your genetics. For some it becomes noticeable, sometimes it doesn't. Maybe look to your relatives on that for an idea.

- Voice changes are a case by case basis. I've noticed guys having really noticeable changes about 2-3 months in, but some guys could be sooner or a bit longer. I'm going to be entering eight weeks on and I'm already preparing myself for a drop since my voice has been getting hoarse.

- Body hair is another case by case basis IMO. You might get a little hair, or you could be bear or hobbit status. Like with the adam's apple thing, try looking to members of your family and relatives for an idea if you're able to.

- I've heard a few guys say they got taller while on T, but it's my understanding that it's less common if you've already stopped growing or your growth plates have fused. I stopped growing when I was about 11, and I doubt I'm going to get taller (doomed by short relatives from the start).

- That's going to depend on your situation and the state you're in. Some doctors aren't comfortable with giving hormones to people under a certain age and some are. I think the youngest is 16, but you're likely going to have to jump through hoops for that, even with a good doctor. For minors, you're very likely going to need consent from your parents (maybe both, but it depends on state laws).

- It's never too late to transition, but I feel they say it's best to do it while you're young because some things might be easier to manage if done early.

- Emotionally, it depends. Some guys said they're quicker to get angry and others said they're calm and rather zen. For me, I haven't noticed too much other than feeling sad and a bit depressed; but I blame a lot of that on current stress and the weather.