So drawing about 30mA from it is causing a voltage drop of 0.5V. Not a very stable voltage source then! But no surprise, voltage regulators are not meant to be used that way. I would not use/rely on it at all. Stick to the using 5V output to power other circuits, or if you need to draw > 0.5A, add your own regulator direct to the 6V source. Use a "low voltage dropout" type, because an ordinary 78(L)05 really needs at least 7V input to give a reliable 5V output.
But we are still no closer to an answer as to why your PC crashes when you unplug the Arduino from USB, or why your diode stopped this from happening. I have no ideas.
Paul