power problems?

So in my micra at the moment I have a pioneer head, 2 soundstream rear6x9 300watt speakers, 2 pioneer front 6" 120watt speakers. All speakers running off a pioneer 600watt 4channel amp. The first time I drove it home from an autobahn installation the amp was up full power, 120a fuse in-line on amp power cable near battery, equaliser set for kickass rock music (not much doofdoof) playing at about half max volume and the car just stalled at neutral at the lights around the corner.

Took the car back, they messed with the amp (changed the gains and power consumption) and gave the car a test drive and it was fine. But now whenever I turn on my car the first second its idle is sweet, then the head unit lights up and I guess the best way to explain it is that the car feels slightly drained of power :/. It just feels like the car revs slow down, almost to a stall for a second. I'm sure my sound system is affecting my car performance, what exactly is the problem and how do I fix it?

I have a stock battery and alternator, should I upgrade both?