tl;dr I haven’t seen anything here I consider an improvement on the current system.
If you really want to pursue it, we need to make skill handling more modular and put the new skill system in a mod.
Speaking of arbitrary 
The number of skills reflects how immediate and central the activity is to the game. Few activities are more immediate or central to the game than gun handling.
How do any of the alternatives improve it in any meaningful way? If you merge shotguns and rifles, the minigun still won’t fit in either.
Yes, it is, in the ways that matter to the shotgun and rifle skills.
That’s not arbitrary, it’s a question of how it’s handled, not what the ammunition is. If it’s fired like a pistol it uses the pistol skill, whether it’s a laser or a shotgun or crossbow.
This is a symptom of our disagreement about what game balance means, IMO “some skills are more valuable than others” is not just acceptable, it’s a tautology.
e.g. bows are not balanced to compete with guns if you aren’t in dire need of either conserving resources or silence, if you don’t need eiher of those, guns are better in every way.
Working as intended.
This is an implementation detail, it has nothing to do with the system as a whole.
Seriously? Making it arbitrary is somehow an improvement?
This one actually has some potential, but good luck turning it into a consistent system the player can actually understand and interact with in a meaningful way.
The core of the skill system is that player actons trigger practice which improves skills, how are you going to map player decisions to those categories?