The video recording time depends on the size of SDHC Memory Card installed. I use a Sandisk Ultra SDHC 32 GB (Class 10) card that's large enough to last for months. Remember the device re-records (loops) over older footage, so if you need to permanently to keep a particular video, select, copy and store it on your Computer. In my case its 'fit and forget' device that unless an incident occurs, do I only then retrieve the footage from 'Road Runner' as required.
Sounds like a faulty unit. You could try taking the battery out and reinserting it. Does it still record? Your statutory rights to a refund or replacement should not be affected by not sending back the warranty card - in my experience this is only so they can get your details to bombard you with junk mail and spam. Contact the vendor and explain your issue, I have found vendors trading through Amazon Marketplace to be very reasonable and obliging, having had an internet radio and desktop PC both replaced with no quibbles. Good luck.
Using the mount supplied I located it just forward of the rear-view mirror. The wiring was fed under the headliner down to the drivers position then up under the steering wheel cowl to the 12v socket (used to be called the cigarette lighter!). The system takes over from there - switching the camera on as you start the engine and, after a slight delay, switching off as you park up.
Yes. The camera can be set to record or not record sound. I find with my recordings that the background of Radio 4 is prominent. One word of warning though - you cannot easily stop it recording if you and passenger(s) are talking about some third party - this is also picked up.