Welcome to the game
Why don't the Cleanup drones, for witch I have not found any use, increase the efficiency of a planets scrap rate?
Because I haven't yet heard or thought of a way of integrating them into the process that would not cause substantially more fiddliness than fun.
And what does?
Each command station type has its own efficiency:
Home: 50%
Econ: 5/10/15%
Logistics: 10/20/30%
Military: 4/8/12%
Warp-Jammer: 10%
That's the only thing which impacts the rate.
In general you don't need to think about the salvage mechanic in an ongoing way for it to work for you. You make decisions about where to take the majority of AI attacks (you may even dare to take them on your homeworld to greatly increase your effective salvage) and which command stations to build and which (if any) to upgrade.
So, like the other economic mechanics, knowledge of the system and careful thought is helpful (and, taking all the economic stuff together, quite necessary) but the majority of your mental effort is supposed to go towards your military strategy and the execution of that