I don't know the answers to your questions for sure but since no one else answered you I thought I'd share what I would do and in fact may do on my own. The way I would approach this is to get a charged battery that I could use for testing and hook up a cheap switch to the trunk popper and have a pigtail that I could put to the hot side of the battery. A quick touch to the positive terminal should tell you which wire to the popper needs power. Then I'd route a wire to the factory switch with an inline fuse where its easy to get at. I like your idea of the radio as a take off point for the power. You don't want it live when the ignition is off in my opinion so the radio is great. If you do want it on all the time trace back the hot lead for a clock or light switch and use that instead. Also what I'll probably do is use an after-market kit and that will probably have better directions. I don't think they are terribly pricey so you may want to get on of those and use your factory parts in place of the aftermarket ones to the extent possible.
I hope that helps.