Hey

A lot of your answers can be found in the entity files you can download from the sticky in the strategy forum. I'm by no means a good player, but I understand some of these things, so here we go:
Vertigo is AoE, aoe ranges are 2000/2500/3000. For comparison's sake, the Disciple has a fire range of 3500, so at level three the radius of the circle of Vertigo's AoE is only slightly smaller than that. That's a pretty big area.
Reverie is probably the most overpowered capital ship ability in the game right now, due to what I perceive of as a bug in 1.03: you cannot attack a ship under Reverie anymore. Even if you could, it's damn overpowered: its duration is much longer than its cooldown, and at level 3 it has an AM cost of 50, meaning that after the duration that much AM will have regenerated. This means you can keep an enemy's capital ship fixed in place for as long as you want to. This is a game-winning ability.
As far as I can tell, firing weapons counts as an ability for purposes of buffs, so yes, Guidance should increase dps.
Telekinetic push does deal quite some damage to ALL fighters in range. At level 3 it deals 40 points of damage, which is enough to kill an Advent fighter. This means if you have three advent fighter squads in your range, you will kill all 27 (!) fighters instantly. This will take your enemy forever to rebuild. On top of pushing strikecraft away from your carrier, it also badly slows them for 15 seconds, which is not a defensive aspect at all. Slowed fighters, if they end up in the range of flak frigates, are instantly killed. The fighters' great speed is their main survivability factor.
Anima Tempest creates 30 fighters. This is three squads and change. I GUESS it creates fighters, not bombers, but I'm not sure.
Resurrection lifts one of your capital ships to the level of any other capital ship you previously lost. Note that this is only useful if you had three or more caps. Example: Cap A is the progenitor. Cap B is some cap at level 5. Cap C is a freshly built cap at level 1. Cap B is destroyed. You cast resurrection on cap C and suddenly cap C is level 5. Note that I agree with you: this skill is nearly useless. It's way too contextual and as such useful only in very few situations which are not likely to occur in a serious competitive game. You can hardly plan to lose a capital ship...
Remember how I told you that telekinetic push is very strong at level 3 for inflicting 40 points of damage? Well, flak burst inflicts 30/45/60 points of damage. This means at level 3 it instakills every Advent strikecraft, all Tec fighters (not bombers, but those are seriously damaged, down to 40% of hp), and it seriously injures all Vasari strikecraft. In short, DO get this skill when you go against Advent (who have many WEAK strikecraft) and use your AM differently if you're going against Vasari.
Radiation bomb does damage to unlimited targets, but the AoE range is not very large: 1200. It does the displayed damage only to the main target (125/250/375). To everything else in range it does damage every 2.5 seconds for 20 seconds. The amount of damage it inflicts is dependent on the level: 7/14/21, meaning that if a target stays within AoE range for the entire duration it takes between 56 and 168 points of damage. I'm a little worried about how their event model works: if the main ship dies before the duration is over, does the damage still proc? This I can't judge without looking at the actual source code.
Missile Barrage fires 20 missiles which hit for 150 damage each. The range is huge: 10000. That's a little less than the overpowered LRM range in 1.03. Remember this is the radius of a circle, so it's that range in all directions. I'm nearly certain that I'm reading something wrong here, because this would mean that ability does 3000 points of damage, and that just sounds wrong.
I'm not sure how magnetize works. If I'm reading this right, it pulls 8/12/16 strikecraft into a target for 25 damage each. I'm not sure what happens to the strikecraft afterwards, but if I read this right if a target manages to attract 16 strikecraft before the 10s duration runs out, that would be 400 points of damage (and maybe 16 strikecraft destroyed?) This is on par with most other damage dealing skills. Again, this seems like a useful skill to use against Advent who have so many strikecraft that your chance to attract the right amount before the duration runs out is highest.
Weapon Jam is pretty much the ultimate anti strikecraft ability from what I'm reading. I've yet to use it (I rarely have enemies going strikecraft against me), but from what I can see here it would enable you to deactivate enemy strikecraft in range indefinitely. Its cooldown is 15 seconds at all levels and the duration is 15/25/35 seconds.
Phase Out Hull is another VERY, VERY strong skill. You're overlooking the fact that it can be used on friendly capital ships. There is nothing better for improving your capital ships' survivability. Weapons already fired at the cap when you phase it out also just disappear, so it's a very good panic omg my capital ship is in trouble skill. At level 3 this makes your capital ship invulnerable for 10 seconds. Also, if you use the skill offensively, note that its duration is higher than that of Ion Bolt and that unlike Reverie it cannot be interrupted. Of course Reverie cannot be interrupted right now either, but I believe that to be a bug. I should probably post a thread about that.
Distort gravity is amazingly useful. There is no better get out of prison free card in the game. Whenever you find a battle turned against you, you use this skill to get away with minimal losses. When there's an enemy capital ship almost dead running away from your fleet, you use this skill to hunt it down before it can get to a repair bay. It's hard to think of a situation where this skill isn't incredibly useful.
Subversion I haven't used either, but if I'm reading it right this is essentially a better version of FarSight or whatever they called the Revelation Battlecruiser's spying ability ingame (internally they refer to many skills under the name of the original war3 skill

). I mean, its range is not infinite, but you spy for a longer time and you also slow down build speeds. In a 1v1 early rush scenario this can be game winning once more if you can pump those tier 1 ships out faster than your enemy.
Finally, stabilize phaaaaaaaaze space (oops

) simply transforms your capital into a phase gate. This means that ships from another system with a phase gate can jump IMMEDIATELY to your ship. This is the only skill of this kind in the game and can turn a lengthy campaign where you often have to wait for reinforcements to make their long way to you into a Blitzkrieg. Again, one of the most useful skills in the game.