Boosters are 100% modifiable, just like other equipable gear, so... should actually be possible, yeah. A hierarchy might look something like:
Make a new effect group, possibly under qualifications, for carrier_boosts.
Equipping the actual carrier hull sets the effect carrier_boosts = 1, which would show as Carrier Modules = OK
On the actual boost item, the requirement to equip would be carrier_boost = 1, plus any other requirements you had skill-wise. The attribute desired would be consumables_structure_repair_ value, which I believe is set in HP/second.
The other option you would have would be to make it a device instead of a booster, requiring manual triggering, but I haven't tinkered much with the scripts for those. I can actually test out the above solution a bit later, wouldn't take long to rig it for a test ship and see. 
As for the actual fighters, I could see two ways of doing it: either make sure the carrier saved one weapon slot for a 'personal defense turret', or rerig the drones to be devices instead (again, should be possible, but much more intricate to code) and leave all the actual ship weapon slots as guns it could use to defend itself. I actually kinda like the first option more myself, though, because I would assume that the balancing aspect of the carrier would be a weak personal defense. You could perhaps give it like a single II or III energy mount on a 360 degree arc atop it, allowing it to mount a beam weapon and giving it some defense against missiles much like a CIWS/phalanx would.
BeLugh might have better options, though. I think he's delved quite a bit deeper into the device scripting than I have.
A mix of both boosters and devices makes the most sense to me, have some passive abilities and some active abilities.
So we could have boosters that give the effects mentioned? Like the passive hull repair for the Dominator.
Or the Carrier could have a "Repair Drone" device which would basically act like a high level structure repair consumable that recharges.
Actually...having all "drones" as devices seems to be an intriguing suggestion, you could basically say that those are like the "Hangar Bays" for the ship and you get to pick and choose what you want, like...2 bombers, 2 fighters and 2 repair drones....or....4 bombers, 2 fighters.
Customize your ship a bit.
Is it possible to make a device act like the weapon you described? Where it spawns a drone that fires missiles before kamikazing?
Because IMO, that would be the ideal solution...which leaves the weapon slots for just basic guns the Carrier can use to defend itself.
Oh, and the one gun that I had, the level 2 Ballistic mounted near the rear was actually modeled after a CWIS.
I didn't tinker with boosters yet.
For devices you can definitely implement a heal. But i am not sure if you can make it a heal over time which looks smooth.
But it is no problem at all to make it heal for example 20% of max structure(hp) and add a cooldown (like 15 seconds) on it.
A device with heal over time is possible as well (but i did not tinker with the timemultiplier yet), but devices always need to be activated.
Something like that could work with the above system....could you like....have a device called "Repair Drone"
which does like... a 1% heal every second for 60 seconds?
Then has to cool down for a minute or something?
I would like to have them differ from consumables in some way, besides the fact that they have infinite uses.
Hmm....would it be possible to have it as a targetable device?
For instance....target another ship, activate the repair drone and repair them instead of yourself?
That would make sense considering it's a drone and would make it more useful than a simple consumable.
For boosters you can for example modify calcucateship.js to check whether you have one or several of those boosters equipped and then add a heal
(In calculateship not just all effects but also fuel usage is written in. So it would be executed as often as fuel gets calculated and everything else)
That would be better for something like the Dominator, which has a base hull regen over time.
Bigger problem would be to have a nice animation for repair drones repairing your ship!
Yes, I would LOVE to see that, a cool little animation of a repair drone fixing up damage.
For offensive drones i was thinking about carriers already. Having a squadron with others assisting you would be easier. When you have a carrier they need to dock and accept orders
For example devices are used to give orders: attack, move, mine, dock on carrier, follow me
That's more along the lines of what I was thinking, have the ability to make your own little squadron of fighters/bombers and then maybe like a unique "Kamikaze Drone" weapon.
The carrier could have 1 missiletype weapon. When fired it starts one fighter, it would have like 3 sec cd as they cant start at the same time. When one of them docks, ammo gets refilled. The fighters would needed to be saved in a n array (or structure array to store if they are docked ->repair), saving at least the hp of the fighter. When one is dead he cant dock on ship->no refilled ammo until you dock on a station
That'd be perfect if it could be combined with the repair drones.
Launch your attack ships and then use repair drones to keep their health up.
Making the Carrier a very "supportive" unit....whereas the others are more offensive.
devices for attack move and mine will have a target (like mining lasers) follow and dock are just usable like consumables
If we did make them as devices, you'd definitely want an alternate method of mining as I'm sure no-one would want to waste a valuable hanger bay slot for a mining laser.
