Residual-current device: Would a big coil trigger it because it stores electrons?
What if I connect a big coil? Because of the inductance it would store a certain amount of charge which is released later on when it is disconnected from the voltage source.


If you disconnect a "charged" inductor it will arc at the relay contacts to "discharge". It obeys normal circuit rules.


  Would the missing amount of charge be able to trigger a RCD? Because the RCD would see only some charge flowing into the coil but not coming out again right after connecting the coil?


Current is like water in a closed loop pumping system. You can't have current in without current out. The inductor doesn't store current - it stores magnetic energy.


  What would happen if I connected a big capacitance?


This time the energy would be stored in an electric field. Current in = current out.