I'm currently breeding Tyrogues on LG because my Diamond is in storage. When I finally transfer it over, when I evolve it, there's a 50% chance of Hitmonchan learning either ability, correct? Also, if that's true, if I save right before evolving it, if I don't get the ability I want, will resetting and trying again reset the chances?
Yes and no on the first question. No on the second question. I'll explain.
You see, when a Pokemon is created, it is assigned an "ability slot" based on the value of its PID (process identification) number. If the number is even, then the Pokemon will have its first ability--let's call that Ability1. If the number is odd, the Pokemon will have its second ability--let's call that Ability2. This never changes.
In many cases such as a 3rd gen Tyrogue, both Ability1 and Ability2 are the same and you won't be able to tell the difference. If the Pokemon's evolution has two abilities, you won't know whether your Pokemon has Ability1 or Ability2 until you actually evolve the Pokemon. However, because the ability slot is set, that particular Pokemon's evolution will ALWAYS have the same ability.
In the case of 3rd gen Tyrogue, when you Pal Park it and evolve it into Hitmonchan, there is a chance of the Hitmonchan having either Keen Eye or Iron Fist. However, that Hitmonchan will ALWAYS have one of those abilities and not the other.
[I'm bolding this part because this is the main point:]
If you evolve Hitmonchan, looking for Iron Fist, and get Keen Eye, then you're going to have to Pal Park another Tyrogue. That particular Hitmonchan will always have Keen Eye.
When you can breed in Diamond, though, I would recommend doing that instead of breeding in LeafGreen. (I'm assuming you don't have Emerald and its limited IV-checking capabilities.) 4th gen Tyrogue has two abilities so it's much quicker to breed for the desired ability since a Guts Tyrogue would always evolve into Keen Eye Hitmonchan and a Steadfast Tyrogue would always evolve into Iron Fist Hitmonchan.