I once knew a guy who put a 10 inch sub in the floor board behind the drivers seat. No box or anything just sitting in the floor and he just spliced off one of the rear speakers. Any ways this thread made me think of that. Yes you HAVE to have an amp if you want a sub to sound like it is supposed to. If you want to get more bass with out adding an amp then you need to replace the speakers that came in the car, and even then it is a good idea to get an amp. but if you just hook up a sub by splicing the wires going to one of the speakers will probadly not even be able to tell that it is there. the factory system DOES NOT have the power to push a sub.
as far as a remote wire you need some thing that is on when the radio is. i used my power antenna hot wire. as far as splicing into the rear speakers i guess you are talking about an out put source for the amp. If you still have the stock HU you will need a line out converter. Then you just tap into one of the speaker out puts, you can do that before or after the factory amp. I would recomened that you do the connections before the factory amp but that may just be me. Hope that answered your questions if you have any more then just let me know.