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 NAND gate can have two or more inputs. The o on the output means not showing that it is a Not AND gate. The output of a NAND gate is true unless all its inputs are true.
This type of variable capacitor is designed to be set when a circuit is made and then left without further adjustment.