Power Arduino via USB without computer [Question]

The 5V on the USB cable simply connects to the 5V rail on the Arduino - its equivalent to directly powering the 5V pin.

There is nothing wrong in powered the Arduino via the 5V pin - but you must ensure it is a regulated 5V which never ever goes above 5.5V or so... If you have a cheap-and-cheerful "5V power supply" its up to you to verify it does actually put out a well-regulated 5V. You need to measure it with a multimeter under no load and under load (not your Arduino!) to check the DC output is 5.0V +/- 0.1V and that the AC component is small (< 50mV is advised).

If you use a switch-mode 5V power supply it may be quite noisy - which can be fine except that analogRead() values pick up several LSB's of noise.

Beware any cheap power supply from ebay, you may be taking a gamble with quality (understatement).

Also some power-blobs are sold as 5V regulated and aren't regulated... beware.