Upgrade alternator? No idea, don't know what you're driving. Use a cap? Don't bother.
You should be able to tell pretty easily if the amp will power the speakers. Look at the power ratings (in RMS). See what power the amp can deliver at (depending on the impedance of the subs) 1ohm (2ohm subs connected in parallel) and/or at 2ohm's (4 ohm sub's connected in parallel). I could look on the net for you, but I think you could do that .