How long does the bootup take?
From a full power-down (i.e., power completely removed), about ten seconds on my Mark 1. Probably similar on the Mark 2.
From standby mode, about 0.000000 seconds.
Shut down?
Exactly 0.000000 seconds.
Do I have to tell it I'm about to shut down or does just turning off the car do fine? Are there any other issues related to this that I should (would want to) know about?
No, just turning off the car, or even yanking it out of the dash while it's playing is just fine. It doesn't need to be told to shut down. Although, if you want, you can manually put it into standby mode.
It's designed to shut itself down gracefully when it loses power, so there's no issues related to that. It only needs a couple milliseconds to save its current state to NVRAM, which it does when you shut it down or when it detects it's had the power removed. Sort of as a "last dying act", if you will.
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Tony Fabris