It depends entirely on how much current is being drawn from the battery by the device.
Because charging a laptop and other devices are pulling from volts, not amps, the best descriptions I can give is on the project page.
Here's an example: 2000 mAh is the same as 2 amp-hours, meaning the battery could supply 2 amps for one hour, 1 amp for 2 hours, a half amp for four hours, and so on.
So how much current does your device draw? Let's say it's 100 mA (0.1 amps). From the above, you know the battery can supply 1 amp for 2 hours, so it can therefore supply 0.1 amps for 20 hours.
The answer for the second part of this question: Because the battery is not being charged via USB (5 amps or less), it takes less than two hours to completely charge the battery!