1. you are correct, the remote turn on should be attached to the power antenna lead at the remote/antenna wire from the radio. So that is safe
2. How are you interfacing with the factory amp. Because you have a factory amplified system, and you are using an aftermarket headunit, you are in a mannor of speaking double amplifying the speakers. If you did not use a signal converter, what you are experiencing may be the low level noise from the deck being amplified by the factory amp.