You'll need a full length of low-gauge (very thick) wire run from the battery to power the amp. It pulls far too much current for any other power source.
I saw a write-up that mentioned that the antenna in these cars is powered. And only when head unit is on. So you should be able to find the wire you need right there in the trunk for a remote turn-on!
The radio antenna? I wasn't aware that it was powered. Do you know the reasoning? I only ask cause the only powered antennas I was aware of we're the ones that go up and down.