Yes, that Asus charger should work. 330ohm resistor to LED should be good. That’s a fairly common resistor size for LED’s. With LED’s, you’re basically controlling the current flow.
And an FYI, there are 5VDC relays available. Such as these:
http://uk.farnell.com/omron-electronic-components/g5v-2-5dc/relay-pcb-dpdt-5vdc-2a/dp/9949488
You can use an imp pin to drive the relay(s), or any 5V load, via a switching transistor (2N2222):
