To answer your original question, you "can" increase the power output o the sub by hooking up both of your rear speaker leads to it, but there are several issues with doing this. The main problem is that you could (depending on how you have wires the sub in and the impedance of the sub itself) end up putting too little of a resistance on your car's head unit. This can make your deck head up and damage to it. As for power output, even running both rear channels your sub will only be getting an rms (continuous power output) of around 20w, where as your amp will likely give you that tenfold (200w+ depending on the amp that you have). Other then this you are also not going to be getting a very good sound out of the sub, as it was designed to only play low frequencies (low bass and kicks) so you will end up with a really muffled and muddy sound. An amp will have a LPF (Low Pass Filter) which only allows the "low" frequencies to "pass" to the sub. This will sound much much better.

As for installing your new deck, if you are bent on doing the work yourself, you simply need to got to your local car audio store and they will be able to sell you a harness adapter. This will need to be wired in to the harness on your new deck (so soldered or cripped) but will plug directly into your existing harness going into the back of your factory deck. This will save you cutting and messing with anything factory, so you don't really need to worry too much about messing things up. (everything is colour coated). As for installing the amp, this is much more involved, and I would honestly recommend taking this to a shop to get done, or finding someone that has done these before that can walk you through the process. If an amp is installed improperly this can cause a good deal of headaches for you. Anything from dead batteries to annoying electrical wining from the speakers when your driving, to fires. Hope this helps!