a scanner system module that can FSS and map planets in the current system.
A control panel of new FC bridge where you can set a target and launch a satellite (one would have to calculate the trajectory and necessary gravitational maneuvers to reach destination planet - sort of mini-game), then via telepresense launch scanning probes from the satellite to scan planet surface. The satellite may be destroyed by pirates, or crush into a planet or simply miss the planet due to miscalculation (failed mini-game). Each satellite will cost credits to restock to make proper trade-off.
a module that houses a mining crew that will go out to the resources in a system and bring it back to the carrier.
So one would need to deploy FC nearby the ring (possibly at the very close proximity of resource site or hotspot, like 10km). FC will be frequently attacked by pirates and player will have to defend FC and also transit drones which will move mined resources. This way only very common resources will be mined and to improve it player (or teammate) will have to fly and launch prospector limpets. Again trade off between restocking transport drones and efficiency. Harvesting hotspots in unpopulated systems would require active prospecting (due to lack of pirate activity).
a module for fighters that the player(s) can launch and fight with in the instance.
FC can drop on the combat zone and give players the ability to restock ammo just landing on FC (without leaving the instance). This will attract more enemy forces, who will try to re-route FC out. When all teammates are on the board of FC and combat zone is won it will trigger respawn. FC owner can call for support (fighters from FC), but each fighter lost will lead to need to produce new one paying its cost including outfit. Each support call will trigger enemy response and fighters kills won't count as combat bonds (only combat zone wins). So no AFK, as fighters are only play a role of combat support to FC owner fighting that CZ.
a navigation module that allows the player to move a carrier in regular space. Either by manually flying the ship or by plotting a course to where the carrier should end up.
With significant FSD cooldown and all the ships being locked. May also require proportional Tritium consumption (like jump out and back in) for each supercruise jump. I would like to see it maybe as route planner for alternative mode of system map.
a search and rescue module. Not sure about the details...
Bring escape pods on FC and get not only credits for escaping, but also some random bartender materials traded.
a factory module that can be set to use resources the carrier has on hand to build ship modules and ship hulls for sale. Or even for other things, like weapons and stuff.
And generate regular fix and restore missions for FC owner and visitors. Like source and return power regulators etc.
the ability to hire engineers and you have to increase their abilities like a crew member.
Could be a missions from engineers - move to distant system and mine resources or scan anomalies. While on that mission - the engineer representative may be available at the FC providing similar services as original engineer, but one or two levels less (depending on mission conditions).
I am pretty sure everyone can came up with ideas how to implement original suggestions in a way to limit exploitation.