What I don't understand yet is that the Marants PMD660 says it uses 0.8A while a USB battery only gives 5V 0.5A. Doesn't that mean a cable that can connect USB to 5v DC won't be enough or does your cable somehow increase the current?
I think you're confusing the USB minimum standard (.5 amps at 5 volts) with the actual output of the battery. The spec sheet for the battery you found lists the following:
What are the power requirements for the devices to be charged?
The Portable Power Max will charge any device with a maximum current
requirement of 2.5 Amps. As an example, the iPhone requires maximum 1
Amp. However, when multiple devices are simultaneously charged
together they must not exceed 2.5 Amps in total. The voltage requirement
of each device charged must be 5 Volts.
Thus, this battery (and any battery that will charge an iphone 3 or 4 which require 1amp of current to charge) will have no problem providing the current (amps) needed to run the PMD660
Hope this helps