if your going to stick with the speakers you have then you wont need another amp, the headunit will be fine as JVC units rock anyway.
if you did need some extra front sounds, which with your sub i would recommend then you 'could' get away with splitters to the amp for the componants but they are really only for sub useage because you will lose your stereo sound, which, for subs is unimportant but for componants it is, if it will bother you ( depends a lot on the music you listen to)
as for controling the splitters, just think of it like it is, you will basically have two left sides and two rights but unless your amps are very close together it will be hard to get the seperate lefts and rights into the amps because splitters arnt very long ( or at least mine arnt!) and most of them that ive seen go on the amp end of the phonos.
you can get splitters that work the other way round where they split at the headunit and you have two sets of phonos going down the car which would solve your problem, its just getting the right splitters for that can be a pain and the fact you need two sets of leads, if you use Ebay or other net shopping it shouldnt be a problem though.
if you need any clarification on the phono thing or anything ill PM you my MSN address and ill help, it can get a bit confusing!
is the amp you have 2 channel or 4? ( does it have 4 speaker output terminals or 8? ) if it has 8 you wont need another amp, i should have said earlier. if its the exact amp in that picture you will need another though, but i know they made a 4 channel too, so thought i would just check.