Personally, I'd change it to Fort and Will are both good.
Instead of replacing Bravery: At 8th level, the fighter becomes immune to fear. In addition, all allies within 30ft of the fighter benefit from his bravery bonus against fear.
Or something like that, basically a non-magical aura against fear.
Heal is a pretty useless skill, so I don't have an issue with giving the fighter a bonus to it, but I think it should only apply to himself and allow him to give long-term care to himself.
I do feel as if the fighter should be limited to combat feats instead of opening up his bonus feats to everything, but that doesn't mean you couldn't come up with a short list of specific non-combat feats he could take as well.
Class Skills: (if I were to alter them)
Bluff, Climb, Craft, Diplomacy, Escape Artist, Handle Animal, Heal, Intimidate, Knowledge (Dungeoneering, engineering, geography, history, local, nobility), Perception, Profession, Ride, Survival, Swim
The evasion for fort reminded me of something, but at the time of my post I couldn't put my finger on it. But I remembered, Mettle, an ability from the Hexblade or the Pious Templar from 3e D&D
Mettle (Ex): At 3rd level and higher, a hexblade can resist magical and unusual attacks with great willpower or fortitude. If he makes a successful Will or Fortitude save against an attack that normally would have a lesser effect on a successful save (such as any spell with a saving throw entry of Will half or Fortitude partial), he instead completely negates the effect. An unconscious or sleeping hexblade does not gain the benefit of mettle.
Mettle (Su): A pious templar's special blessing allows her to shrug off magical effects that would otherwise harm her. If a pious templar makes a successful Will or Fortitude saving throw that would normally reduce the spell's effect, she suffers no effect from the spell at all. Only those spells with a Saving Throw entry of "Will partial," "Fortitude half," or similar entries can be negated through this ability.
I don't think it would be unreasonable for a fighter to gain this at 12th level, especially if the good saves were changed to Fort and Will. I could also see them getting it a bit earlier as well, say 8th level, and get Improved Mettle at 16th level.
Improved Mettle: If you succeed on a Fortitude or Will save against a spell or effect with a partial effect on a success, you instead suffer only the partial effect on a fail. On a successful save, you suffer no effects from the attack.
They won't have evasion, which is much more helpful, but it's a nice unique thing Fighters could have.
I'd argu an unchained fighter should be tweeking what there already is, addimg, instead of remapping and substracting from him, so that old archetypes and existing options still apply to him. Make him like unchained Rogue instead of Fighter, if you will.
4 + Int should be default for all, but I don't think fighter needs any extra class skills, except for, maybe, perception, whatever 1-2 skill he needs as class skills - can be taken with traits.
Leaving 1 save good is fine, later on options with AWT boost fighter saves considerably.
Making bonus feats any kind of feat doesn't make sense for a fighter, an iconic battler. Maybe add a chosen set of thematic general feats.
1/2 level into heal and local also isn't too intuitive for the base model of Fighter. Giving 1 + 1 ever few levels to one of few fighter non-mental skills as a choice would flavor him better and allow to specialize in something.
Endurance for free is thematic, I approve of that.
Removing bravery removes everything that uses bravery. The above mentioned choices are a bit better IMHO, but'd argue it's better to make fighter not immune but able to reroll saves vs fear, he's not divine-infused unshakable paladin, but just a real tough bad-ass who can get himself together. Later, around 14, become immune to shaken vs those of his level or lower, and make him immune as a capstone.
Inquisitors stalwart ability but without armor restrictions is also thematic.
Anyhow, I think Advanced Weapon Training and Armor Training made the base fighter one of the better martial in the game, those were his "Unchaining". He's be great with just 2 extra skill points really.
Adding more skill or feat options isn't going to do much for the fighter. It's the additional skill points and feat slots that are going to improve the class. There's already plenty of thematic options for them, they just don't have enough points and slots to utilize them as much as they'd like. Better to not open the door to adding non-thematic or debatably thematic options when it's really not going to do much for their power level.
A fighter's issue is usually that it can't do the same amount of damage or affect the same level of battlefield control as most of the other classes. Options to improve that makes most people feel that the fighter's flavor changes too much. However, a lot of the more popular options are things that let the fighter have a higher chance of resisting enemy battleifield control abilities, which I think is the way to go. Don't try to increase the fighter's sub-par abilities; just let them consistently use those abilities more than the other classes.
A fighter’s big draw is that you can create many different types of characters. The idea is every fighter can be a completely different character. They are also supposed to excel in combat. Your changes kind of pigeon hole fighters into the same mold.
The extra skill points are not a problem and are almost always suggested on any rewrites of the class. But if you really want to increase the versatility don’t specify what skills they focus on. Give them any two skills as class skills and give a bonus of ½ their level to those two skills.
Likewise give them a second good saving throw of their choice. Create a fighter only feat that functions like evasion except it affects any one of their good saving throws. This feat can only be taken once, and prerequisite of 12th level fighter.
Instead of endurance give them a small list of similar bonus feats to choose from at 4th level. I would include skill focus, and things like alertness. Also included on the list would be lighting reflex, and Iron will, but those can only be chosen if it is no one of their good saves.
Bonus feats should still be limited to combat feats.
Also, a thing I've been pondering, giving the fighter a floating stack of semi-permanent combat feats. Just a few. They can't count as prerequisites for any other feat besides others in this floating stack, but can be changed daily with a 1h workout. Plus add built-in retrainability of the last combat feat taken with bonus feats he gets, akin to Inquisitors being able to change the last bonus teamwork feat.
Throw in the ability to ignore attribute prerequisites or give them the ability that counts as having 13 int and 15 dex for prerequisites, and as combat expertise, and we don't increase the fighters ceiling, but we sure make his room a lot bigger.
One day he can be switch hitter, another he's a brawler, third he speck out for a covered op. Basically the same fighter but the 3-4 floating feats will help in a pinch, like they do for a brawler.
I'm not sure if this would be appropriate for "Unchained Fighter" or not, but one thing that would enhance the fighter greatly which has nothing to do with skills or feats is a more significant options to have truly special "Combat Manuevers" such that you're not just like "I swing my sword". This can be taken too far if you make combat manuevers too much like spells (like they did in 4.0 D&D), but in general I think they are a nice way to make Fighters feel like they actually have special abilities of their own beyond the vanilla nature of just weapon proficiencies, bonus feats and high bonuses to combat.