With the current battery system, obviously, it will depend on the mAh of the battery and the number of watt hours. For a disposable battery, something that's the same size as a regular cigarette, it would last for anywhere between 150 to 300 puffs, depending on the per-second puff ratio.
When it comes to your second question on rechargeable batteries, those rechargeable batteries exist today. They have to be charged either via a wall charger or via a USB charger. Those are typically the technology that is available today for electronic cigarettes.