Right (what poncho said)
It makes a little more sense when you understand that the vehicle is designed to turn off interior lighting due to a door being opened when the vehicle is moving. That explains the first thing you mentioned
The radio staying not staying on is also an indication of same problem (vehicle always thinks a door is opened).
The last thing might have happened if you inadvertently changed the vehicle personalization feature in your vehicle and turned off remote activation verification, however I thought you could only disable the horn chirp If you have your owners manual look that up (page 2-12).
http://www.mygmlink.com/pdf/go2conte...001grandam.pdf
Since you aren't complaining about key in ignition warning without driver door opened I would say the problem is not with your driver door.