I'm assuming you have it setup to go into standby to reduce boot-time.
Depending on the power consumption of your PC while it's in standby, and your battery's capacity, you may find this a problem if you leave it for a few days then come back to find you can't start your car.
You're probably better off hibernating the PC (and doing a proper shutdown and reboot about once a week to clear off any nasty temporary files and the like).
Question 3 I can't help you with, I've no idea what you're talking about.
Hope I've been of some help.