Read
http://en.wikipedia.org/wiki/Motorola_6412 it'll tell you all you need to know about the 6412 and the 3412, inluding the Mute disabling and the 30sec FF. I just switched from the 6412 to the 3412 but kept the same remote so I know the button remapping works on both models.
Incidentally when the unit is switched off by the remote power button (ie front panel lights off) the buffers do stop recording. And yes, if it is off it will come on for the duration of the recording and then switch off. It will always Mute at this point - remapping an unused button on the remote allows you to un-Mute. I have a receiver as my AUX on the remote so the remote Mute button is linked to this.
Order of switch-on (DVR,TV, or the other way round - don't know which it should be) is only critical when using an HDMI - with Component cables it make no difference as there is no handshake. If you use the red power button it switches the DVR,TV and then AUX (keep it pointed at the equipment) so I assume this to be the correct order!