Let me try to clairify: A capacitor consists of two or more metal plates seperated by an insulating dielectric. Current flows into and out of the capacitor as it is being charged and discharged, so it can pass AC but blocks DC. Some dielectrics produce more capacitance than others, depending on the dielectric constant. Air has a dielectric constant of 1, an insulator with a constant of 5 would produce 5 times the capacitance.
The DC leakage thru a capacitor depends on it's construction. Most film and ceramic capacitors have such low leakage that you don't need to worry about it. electrolytic capacitors have high leakage (microamps) but you can still use them for DC blocking as long as you take account of the leakage.
The temperature stability of a capacitor depends mostly on the dielectric. Film capacitors are most stable, polystyrene being good. Ceramic capacitors have a wide range of stabilities, ranging from NPO (negative, positive zero) which is most stable to Z5U which is usually given as +80, -20 % tolerance.
The dielectric in electrolytic capacitors is an oxide on the metal plate. Contact to the dielectric on the other side of the metal is made by the electrolyte. The oxide dielectric is built up in a process called "forming". A limited current is allowed to flow thru the capacitor and as the oxide builds up, the voltage is increased. If the capacitor is unused for a long time, the dielectric deteriorates but can be re-formed. If the capacitor is old and not re-formed, it can blow up in a power supply.