a) How are Battle riders used/ transportet/ assigned to ships?
Build them (after designing them in design screen). Build a ship with a Battlerider carrier section (middle section). When you have both a carrier and BR built, go to battle rider management screen, select ship, and then drag the BR to the "hanger" for that ship etc. Use ship (carrier) like anyother, when you want to launch, click L on the appropiate icon at weapons icon area.
b) How goes the same with Drone Platforms?
Just design the Drone, built a drone ship (carrier) assign drone to ship in design screen. They launch like BR's (listed in weapons icon in battle screen, click L (and R to recover). I've found that if I launch my drones, and let them auto return/recover I can't use them again, however if I give them a chance to make one strafing run, I can recover and then relaunch.
c) ...and with System Defense Ships (do they need a fleet or are they stationed in the system directly after beeing built)?