That thing from BestBuy is a line convertor only. It doesn't seem to have a remote wire in that pic. I presume you would splice into both the right and left (as it apparently has stereo output, and 4 wires coming in). You will have to run a separate remote wire, yes. To install with that, you are going to have to cut wires and splice into the harness.
You can keep the OnStar/Chimes with the unit I have, yes. And you will with that I presume as well. You really should splice into the fronts, instead of the rears though, as you're probably going to have more of the sound being sent to them. Unfortunately, the OnStar/Chime gets sent to the front driver side speaker. But if you're only running subs, hopefully your cut off is set right, and the chime noise won't make it through. However, any bass coming through OnStar will (conversations/directions/etc…).