A great list! Though I'm not clear how you're differentiating several of these (e.g. combat tactics) from skills. This is your homebrew system, right?
Yes.
It's sort of 3.25++. I don't like the direction 3.5 took, though I did borrow some stuff from it.
What would "Tactics" do exactly?
Tactics represents formal training in analyzing tactical situations, deploying troops, and fighting in coordination with others. Among other things, the Tactics skill lets you reduce facing without suffering squeezing penalties (3 could fight abreast in a 10' corridor, for example), it lets you extend your shield bonus to an ally (forming a shield wall), it lets you negate the penalty an attacker with a reach weapon would otherwise have attacking through your square to hit an enemy, it lets you attack with a reach weapon from 15' away under certain circumstances, it lets you negate the flanking status of an adjacent ally, it lets you improve your initiative when you aren't surprised, and at high levels you can improve the initiative of the entire party, it lets you obtain a flanking position from squares that wouldn't normally be flanking, it lets you determine what feats an opponent has, it lets you determine what stance an opponent is fighting in, it allows you to assess from a distance whether a square is difficult or normal terrain as well as what concealment or cover it provides, it allows you to improve your degree of effective cover beyond what the terrain would normally allow, and at very high levels it can negate surprise. Eventually I hope to develop an abstract mass combat system, and your tactics skill will feed directly into that.
And how would what a Fighter does with it be different than anyone else? Or is it that a fighter gets a bonus to that skill?
Tactics is only a class skill for Fighters. Additionally, there are fighter bonus feats like 'Heavy Infantry' that let you take 10 on some of the above, making them 'always works' options from quite low level. Other classes would require expending comparatively more resources to become skilled at Tactics.
Heh. You remember the 2e PHB which listed the legendary/literary inspirations for each class? For the fighter it was Beowulf, Hercules, Perseus, Siegfriend, Cuchulain, Tristan, Sinbad, as well as Alexander the Great, Charlemagne, Hiawatha, Richard the Lionhearted, and Spartacus. That's a daunting list of some mighty leaders!
Yes. And its worth noting that one of the saddest things that has happened to fighters in the last 30 years, is that people invented a Warlord/Marshall concept that killed the fighter leader and took his stuff.
Certainly, something like the Leadership feat...
I hate the Leadership feat. It's not available in my game. It takes a resource that should be a result of play and turns it into mere mechanics. Plus, it tends to do nothing more than slow play down. Worse, it's pretty much a no brainer feat from an optimization standpoint.
the fighter should poach from the bard and have some sort of Inspire ability? Or interface with Dominion Management rules at name level?
Excuse me, but the fighter isn't poaching from anything. The Fighter has always been meant to be the class of the captain of men, the great leader in battle, and the fighting general. Leading troops in battle is part of the job description, and if your fighter can't do that then you aren't doing it right. First edition tried to simulate this through the concept of the Fighter as 'Lord' upon obtaining name level, and by various advantages when founding a dominion, but I think this is well intentioned but moves in the wrong direction. Instead, fighters get access to a Leadership skill, that gives them various options like removing morale debuffs, reducing the duration of fear debuffs, removing the flatfooted condition from allies (Watch out!), aiding others as a free action, aiding others at a distance, buffing the Will save of allies, or at sufficiently high level aiding all allies in range. Plus there are a bunch of Leadership related feats that increase the effectiveness and add other options like buffing allies move rate (Move! Move! Move!) or share a Feat with an ally, for example. Fully invested into Tactics and Leadership, a smart and charismatic Fighter could easily match or outdo a Bard in terms of versatility and power of his combat buffs. And these aren't spells or magical songs - there are at will abilities.
Eventually I hope to integrate the Leadership skill with an abstract mass combat system.
Again, Leadership is a Fighter class skill, shared only with the Champion (think Paladin, but for any alignment). Other classes can learn Leadership and take the feats, but Fighters spend comparatively few resources to excel in it.