- Remove concentration skill. This is presumably already covered by the self-discipline personality trait.
Self-discipline and concentration are similar, but not the same. I don't know how they're implemented in DF, but self-discipline is the ability to ignore internal distractions and desires, while concentration is the ability to ignore external distractions. For example, the dwarf is hungry (or lazy) but is self disciplined enough to keep working. Or the dwarf is working in a noisy environment, but is focused enough (has the concentration) to shut out the noise and keep at it.
- Remove student skill. If the skill is deemed necessary, use other existing skills in the category of the taught skill instead. For instance, a masterful woodcrafter would learn carpentry extremely quickly and an axeman likely would have no trouble grasping how to use a sword effectively. Categories aren't perfect seeing as bowmen would somehow be prodigies in swordsmanship but it's still better than an entirely redundant, unrealistic, pointless skill.
Communication is a two way street--a teacher must present information, but a student has to be prepared to receive it. Some people are quicker to learn than others. A student skill is entirely reasonable. If you want cognate areas, it should be an addition, not a replacement.
- Remove archer skill. There should be no synergy between the different classes of ranged weapons seeing as they are fundamentally different from one another.
Again, I'm not sure if this is how the DF skill works, but an "archer" skill should probably encompass various related tasks like judging distance, picking out targets, timing shots, et cetera. These are going to be universal across ranged weapons.