How has PVP not been fixed yet.

[Vandril]

-Queue times (this will be fixed automatically if the pvp gets balanced and becomes fun, i think)

GC restrictions are the biggest cause of this, hands down. And that's one thing Square has mentioned they're considering dropping. Let's hope they go through with that in 3.2.

Melee and their abilities to work in pvp.

That's not very specific. I play only melee classes in PvP, and they work fine. I assume you mean to say that melee are in a bad spot compared to ranged. Ranged classes are hampered just as much as melee, even if their mobility is better: BRD/MCH lose damage (by up to, what, 75%?) depending on their distance from their target and all casts can be interrupted by any physical damage taken. Specific classes might need rebalancing (MNK, AST, and SMN, perhaps?), but not simply due to the fact that they're a melee or ranged class.

-All pvp skills need to be on shorter cooldown even after they get reduced cooldown with extra AP

No, not all PvP skills need to be on shorter cooldowns. Most might, but the cooldown for Purify is all but perfect as it is. And there are a few others out there that work fine with their current cooldowns. Still, many of the PvP abilities could use a reduction for sure.

-PLD's need to be able to compete with warriors and dark knights, i guess this could fall under the Melee class balance.

They can. PLD are an extremely powerful support class in PvP. They don't do extremely high damage (though they can still dish out some surprising burst), but they have a selection of incredible utility abilities:

• Cover (+ Hallowed Ground) - Can save integral party members such as healers from death due to physical damage.
• Shield Swipe (+ Sheltron/Bulwark) - Can completely shut down a melee for a time with Pacification.
• Flash - Applies an AoE blind. As most PvPers won't overcap accuracy to counter Blind, its a great debuff to lower enemy damage en masse.
• Tempered Will - Can safely risk cliffs without fear of knockbacks for duration. Don't underestimate how much this can matter.
• Shield Bash - Spammable stun. Enough said.
• Divine Veil - AoE, in-combat Stoneskin when healed by party members? Yes, please!
• Clemency - Extremely potent heal that can heal a target and the PLD at the same time.

WAR better due to overpower requiring no targeting and they can just spam it.

Just to note: actually, Overpower does require a target that is also in range.