Is it ok to run a set of led tubes (interior) off the remote wire from the headunit? The power wire for the led box thing has a fuse inline so is it safe for the amp and leds to get the power from the remote line?
no. if they must be triggered by turning on and off your radio, follow the relay|remote wire advice.
If you just want a switch to turn them on and off, come out of your fusebox with power to them. there is almost always an extra circuit or two, you just need fuses and a 12v switch.