You can apply for the ARN, SPL and ASIC at the same time. Just send all your forms/doco's in together.
CASA will send you your ARN, then SPL and lastly your ASIC. I very recently applied and the hole process took about 6 weeks. You dont need the medical certificate to apply for the 3 things above.. I havnt got mine yet.
Was quite disapointed after recieving the SPL, was expecting something for $50...
$160 gets you a shiny card atleast.
Oh yeah in regards to calling, I rekon CASA is quite possibly the best gov org in AUS. Staff are always very friendly and helpful.. I called a few times :P