Rechargeable batteries can be used in the GPS device. The device, however cannot be used to recharge the batteries. When the device is connected to an external power supply, the device will rely on the external power and will not charge or use the batteries that are inserted.
No, for two reasons. Firstly the power supply on the laptop USB won't be powerful enough to provide a charging capacity. Secondly there will be a diode preventing the USB from supplying charge to the batteries (otherwise it would try to charge non-rechargeable batteries with unwanted consequences).