Anytime you do a reduction in wire size, you should re-fuse. So if you want to run a power lead from the capacitor + to your carputer, then you need to put in a fuse of the proper size for the wire you are installing. 40A would be more than enough for a 8AWG wire, just install that within 12" of where the 8AWG wire connects to the capacitor.
It won't hurt anything to run the carpc off the same wire as the amplifier, however if you are pulling enough power with your subwoofer that there is a significant voltage drop across the 4AWG wire (That would be a LOT of power), then it will negatively affect your carputer. Otherwise you should be fine.
Also, if you find yourself needing a capacitor, do yourself a favor and upgrade your car's wiring (Google big-3 upgrade), and perhaps think about a higher output alternator. Fix it right, or don't fix it at all