Ok, I just lost a nice long reply, so I'll be brief this time, that way I won't get upset when I lose it.
1. There doesn't appear to be an OEM connector other than those with the early 2LT, 2SS that have the two ambient lighting connectors. I suspect this was to work like the 4 Pack gauges and it is wiring that would daisy chain off of another part of the car. For example the passenger kick panel area has a whole lot of wires there you could use.
2. Some people have done both. Just depends on the route you want to go. Mine are attached to the ambient lighting which is only a slight bit different than the instrument panel lighting. They can be shut completely off with the dimmer switch.
3. What do you want, the lamp, or the connector? The Door lamps can be found in the ambient light threads, or order 92238395, and snap them into the factory plastic clips on the driver and passenger sides. You'll get a look like this

drivers

passenger
4. Yes if you can find the connector, and most likely that would only be found on the 2LT and 2SS models.
Hope that helps.