A capacitor stores electric charge. It can be used with a resistor in a timing circuit, for smoothing a supply (it provides a reservoir of charge) and can be used as a filter (blocking DC signals but passing AC signals). Unpolarised capacitors usually have small values, less than 1µF.
A NOR gate can have two or more inputs. The o on the output means not showing that it is a Not OR gate. The output of a NOR gate is true when none of its inputs are true.
Electricity can flow only if there is a complete circuit from the battery through wires to components and back to the battery again.