The capacitor's resistance i.e the resistance offered by the material from which capacitor was made and not the resitance offered by air gap between

the capacitor should it be shown in the circuit either in series or in parallel to the capacitor.

Series I think.

This resistance is generally referred to as Equivalent Series Resistance (ESR). See

 

http://wiki.xtronics.com/index.php/Capacitors_and_ESR

Both.

 

If you charge a capacitor then wait a long time and measure the voltage you will find that it's less than you charged it to. This leakage of charge can be modeled as a (large) resistance in parallel with the capacitor.

The ESR limits how fast you can discharge a capacitor (neglecting stray inductance) and the leakage resistance limits how slowly you can discharge it.