[BrianG]

The best place for a 12v line would be the fuse box. There's usually an empty slot that has power but no fuse. Or, piggy-back onto an existing fuse (they sell piggy-back fuse taps). Just make sure the power is on even when the car is off. Randomly probing wires in other places may not be a good idea: at best, they may not power the LEDs or may not have power when you want; at worst, it could be an airbag wire (no need to tell you that would be bad, but those usually are sheathed in yellow as an indicator).

Yes, the door switch is the "ground" connection. Actually, if you look at most of those door switches, they are quite simple with only one wire "input". When you open the door, that wire makes contact with the vehicle chassis (via the switch housing), which is ground.