does a repair ship, hoshiko for example, also repair ally ships?
Can you micro fighters and bombers?
Squads, yes. Not individual ships within a squad.
Do all cap ship powers effect ally ships to?
Not all, but some can. For example, the Halycon's energy weapon cooldown aura obviously will not affect any ship that doesn't have energy weapons.
How do you control each individual ship's power? (Javelis' cluster warhead, kodiak's intercept, Kol's flak burst.)
^ Do you have to do it all ship by ship? click on EACH INDIVIDUAL SHIP, or can you make the AI do the smaller ships powers for you? (not the capital ships, just the kodiak, javelis, etc, etc.)
There is auto-cast behavior for pretty much every ability (I think the only one that doesn't is the Orkulus starbase phase node?). Most are on by default, the capital ship ultimates (level 6 ones) are off by default. In most cases, it's fine to leave the small ships' autocasts on by default, but you can toggle on/off on groups of ships if you want them to save antimatter for a specific ability. For example, Hoshikos have repair and demolition bots. You can toggle demo bots autocast off to make them only cast repair, or have both on auto so they'd cast both.
Capital abilities are usually best left to micro-managing, but can also be left on auto.
Does the AI allow you to "intervene" when you want to? (you set the AI to auto-attack, but you "intervene" to control them yourself.)
Yes. If you leave auto-attack enabled, you can give manual orders at any time and they will override auto orders. Once yours are done executing, ships will resume auto behavior.
How do you control your carriers? When you select them to attack something do they launch fighters/bombers at it? Or do you have to launch the fighters/bombers and control THOSE instead?
Carriers have no weapons, so a right click attack order for carriers is really a move-to order. You would have to select the squads and control those. You can select everything of the same type in the grav well by alt+clicking on a single unit, so alt+clicking on a bomber squad (in the empire tree or the grav well) will select all bomber squads in that well.