[AC Question]

Can my Galaxy S4 be safely charged from power inverter's usb port that is rated at "5volt/500mA DC power to external usb-powered device?

[Canadazeus]

Yes. The USB port standard is 500ma at 5 volts. The only possible problem is the square wave that is used to duplicate a sine wave in cheaper inverters. The more sine-wave-like your inverter produces, the more it costs. Putting out a square wave is very inexpensive, but is not suitable for many thinks you want to power. If your phone charges in the same time and does not heat up, you're golden. Your AC brick charger is normally 5 V at 1000 mA plus. Slow charging is better than fast. The computer port has another use as storage. Frequent shallow recharges are much better than long deep discharge cycles.