the double "clic" thing is the normal behavior for the X3. those 2"clics" you don't like are in fact the protection system closing the circuit to the amp. this is done for the purpose of avoiding a much much stronger "tac" that you can get on a lot of amps when powering them.
it may sound strong, but it really isn't much. the sound of my pico slim powering ON was oh so much stronger, when not nearly delivering as much power as the X3, so I wouldn't want to hear the X3 powering ON without that "protection" system.
consider that the X3 is much more powerfull than your random ipod and the real thing from zero to turning ON would be really loud if not for that "annoying double clic".
from the noise level of those clics, I would say with confidence that there is no risk at all of damaging an IEM with it.
as for Good Sound's X3 dying on you while walking the dog, I would bet for the battery getting disconnected (the older the batch of the x3 the bigger the chances).