XXx My lights dim every time my b hits. I see multiple answers not sure which are facts.. Please help! xXx?

I currently have a rockford fosgate ten inch sub (150 watts at 4 ohms) hooked up to a kicker zx 300.1 (Birth-sheet says 350 watts cas kicker under rates everything :0 ) Everything is wired correctly with recommended 8 gauge wire. Its currently, Battery---fuse---amp---ground with no capacitor. Im driving a 2001 Mercury Grand Marquis (big *** car). I have had this system for about a year and a half and have just noticed that its been affecting my electrical system. When the base hits deep and hard the head lights and dash lights dim. I want to fix this because Im worried that its hurting my poor car. Should I buy a capacitor?? Buy a new yellow top battery?? A new alternator?? All three?? Im sort of lost and all my friends are telling me to buy different things. I was also planning on buying a JBL (350 watt) 2 ohm dual Voice Coil sub to take advantage of the amps full wattage. Would this be a good idea considering the situation? Can my amp push that sub and is it worth the strain on my electrical system? Sorry for so many questions, I just really need some help and I know that some guys out there "know whats up" ;0 I guess im sort of clueless because im a newby at car audio still >_<. Thanks!!