The warblade is T3 because it is versatile due to an increasingly large list of maneuvers and stances, and it gets bonus feats, and to add it's int to stuff. Honestly, I think it's low T3, compared to the other T3 classes. Most people forget that it doesn't get shadow jaunt/stride/blink or devoted spirit stuff unless it spends a feat, although it does get access to both IHS and the ever popular white raven tactics.
I also personally don't like the maneuver classes because I believe their damage is often sub-par - the class wants you to be using strikes, and unless you're going to raging mongoose or need to bypass DR/hardness for some burning reason, you're never going to use strikes, since using boosts, counters, and stances with a feat chain that lets you full attack, ubercharge, or lockdown is generally a better idea. You're going to use Two With One Blow or whatever it's called at low levels, sure. You're going to use Leading The Charge when it's tactically advantageous, sure, because level in damage isn't a minor buff, and charging is probably what you'd be doing anyway if you're using it.
But to be honest, without crap like sudden leap or hearing the air, warblade definitely wouldn't be T3. To reiterate, it's defenses are the diamond mind conc check instead of save stuff, IHS, immediate action sudden leap to break LoS/LoE, counter charge, etc. It's attacks are basic fighter attacks. And it gets to tremorsense and get various bonuses and give other people actions, plus it has class features that add int to damage sometimes and to reflex saves and stuff. All in all, it comes to low T3, because it can cover multiple roles/do multiple things, but it has absolutely no way of game-changing like T2 sorcs do, other than IHSurging away the sun or gravity or something.
#1
HD is 'whoop de fuck'. If the Fighter is using hp to power his special abilities, he needs more hp, so either 1d20 HD, or double con instead of single con. If you're not giving him extra ways to attack/do damage, he needs more BAB than 1/level, but people will balk at that, and it's just a clumsy way of doing it, so you could fairly safely leave it at 1/lvl. He needs more skill points, because he is not a int-based class, and he needs 6-8 skills as is. You could give him all physical skills, knowledge: martial, and profession: soldier maxed out for free if you wanted to, and then 4/lvl, but it kind of cuts down on customization. Might have to do that to cut down on the nards going 'BUT THAT IS THE ROGUE'S TERRITORY OMG HAX' for you giving the fighter 8/lvl. IMO, fighters should either be proficient with all exotic weapons, or they should have proficiency with any 3 they pick.
#2 + #3
Yep. Weapon spec is a useless fucking excuse for a class feature. Woo, +4 hit and +4 damage and a special feat at level whatever to take ten on an attack and be 'hard to disarm'. Useless.
Fighters should get signature weapons that start at +1 and go up to +15 at level 20. They should be able to switch these weapons out with an hour's training, and have 1 at a time at level 1 and 5 at a time at level 20. Give some way of getting plusses that isn't kensai 'everything you use is flaming smoking deathmarking', and isn't 'pick and choose the perfect weapon mods for the next fight!'. My method in the Goddamn Fighter writeup was to let them use special abilities from the base weapon they were holding, at a cost to the +whatever they had from fighter levels.
#4
Basically what veekie said, but fighter also needs to be able to not get instagibbed by effects that daze with stupidhigh DCs (dazing blow DC 25 at CR 7 or whatever, boomerang daze with DC 512489125, i'm looking at you), or stun, or nauseate no save, or whatever. At this point I don't even really care if he can do T2 or T3 stuff in terms of ripping rifts in time and space or whatever, but he needs to not get instagibbed at fighting or he is T4 or worse automatically.
#5
The fighter shouldn't NEED to buff. That's the point. He should be good enough to go into combat at all times on his own, and should, in fact, have faint design flaws which make it so that a lot of his abilities or bonuses don't work properly when he's buffed, so while he realizes a bonus from being Enlarged or whatever, he can't use his Canny Fighter Dodging Trip ability that requires him to be the same size or smaller than the opposition. This is because buffs BREAK THE GAME IN HALF and the fighter shouldn't need that crazy, and furthermore, adding buff spells to the fighter shouldn't break him in half. It should make him mildly better, like, 150% of normal, not 1529012358u32852350982735crazy% better.