Hi Ben,
Great idea, hopefully all the members here will get behind this too
In answer to your questions:
1. On an early DE engine car (which is where I presume budget will dictate you start from), with the right bits you might get as high as 310bhp, but anything over that you're going to struggle without FI. Any of the SC or FI setups could see you comfortably at 360, although it's not impossible that you'd get more than that on even the most basic setup. If you could get a later HR engined car then I reckon you'd get to nearer 340. Of course with either engine you could go crazy with cams etc but then you may sacrifice reliability.
2. You could get down to close to 1200kg I should think, if you're going for a full strip. Couple of chaps on here would have a better idea than me (MrLizard, Bizz, Keyser, Zmanalex?)
3. I believe you can safely chop away the bits you don't want, the 350Z isn't a canbus setup so go crazy!
4. On a road car you'd lose a little torque with a decat setup and NA, but on a race car you'll be at high rpms so no probs there. With decats and a straight through exhaust you'd be over the limit, so a single in-line carbon bike siliencer should work, or anything like that you'd wish to use.
5. No kits that I'm aware of. Personally I'd go with the KW V3 springs and dampers, Eibach ARBS, and some camber/toe correction arms too. Bang for buck, I don't think there's much out there to touch that setup even if you started spending silly money. Proven and reliable, too.