What Make & Model of Remote Starter are we talking about ? Do you have the Manuals (Install & Owners) for it ?
Answers to your Questions:
1) This depends on if the wire is available in the car & if the Remote Starter has "Factory Arm & Disarm" wires on it.
2) Sounds like a feedback problem, but I'm not sure if this is normal with the newer Bonne'*.
Someone else should be able to answer this.
3) There may not be a Positive Parklight wire in the car, but you can switch the current on the Output wire of the R/* (Remote Starter) with a Relay.
I would be better able to answer these questions if I looked at a wiring diagram for the vehicle.
I will try to find one in the next couple of days for you.
92 Bonneville SSEi - Stock - Remaining repairs needed due to neglect by previous owner - ABS/Trac, AC.
Mods so far: Maganflow High flow Cat, Rebuilt */C
Future Mods: Interior swap for Leath, High Output Altenator, Crazy system, Climate Control swap & Custom Exhaust/Intake.
98 Dodge Stratus - Wifes Daily Driver
92 Dodge Shadow - My Winter Beater