Correct, the noncritical cutoff voltage is about 10v, as Hugo said. I think this is in the FAQ.

Correct, if one is having trouble with interior accessories competing for the player's juice, the next thing to try is to wire the player directly to the battery to see if the problem goes away. I think this is also in the FAQ.

Correct, most cars' voltage will drop during/after cranking and the battery icon during this stage is normal and nothing to be worried about. I think this is also in the FAQ.

Correct, adding a capacitor to cover up the occasional dips in voltage will solve the problem, however one should not need to do so in a properly wired system. The only thing that one might have to resort to is a capacitor for is to cover the cranking period if it's a problem.