Both devices can be connected at once (assuming your phone supports it); one as A2DP audio and the other as phone headset. If you get a phone call, the car will mute the AUX (and your phone should mute it too if it is the bluetooth audio source) during the duration of the call, after which, the audio will resume.
As far as I know, no A2DP devices initiate the connection so you have to do it manually. If you have an android, there is an app (BT Volume I think it's called) that will use some weird voodoo to figure out when you're in your car and attempt to connect. I have an app called Tasker and I set it to monitor for the phone's connection and when it sees that, it connects the audio to the A2DP device. I'm pretty sure there are apps for iphone to get around this too.