Its possible its power related, turn the headlights on and see if they dim when the power drops on the headunit. Does it do it when the car is driving along with higher revs? Other then that its most likely a cheap headunit with a fault.
I built a rack for my 2 amps and placed it where the old bose sub went leaving the passenger glove box free. You could do something with the 6.5" subs but would need to find a way to make an enclosure for them. A small box under the strut still leaves a decent size boot.
Use this thread to work out the wires......
http://www.350z-uk.com/topic/14773-got-the-headunit-out-but-what-is-this-connection/
Looks like who ever did it cut corners as they didn't want to pay for the plug and play loom. I would start over by reconnecting all wires where they've been cut and also check that the speakers are using the factory wiring not the red and black stuff you have there.
I think he's got the stock no bose system so no RCA's. I would pull the headunit as its easier and wire a speaker directly to the back to check each speaker output, then i'd move to the rear speaker once i know the headunits not at fault.
Are you trying to play your tablet through the head unit. If so you need an aux input on the head unit. I dont understand what your saying about your amp.
Its nothing to do with the antenna wire, you need to make sure the earths are all wired up including the extra earh wire to the chassis that turns on the bose amp as the standard bose system grounds through the unit. Some people get lucky as the antenna is enough to earth the system but you should do it as in this guide....
http://www.350z-uk.com/index.php?showtopic=30112
It could still work if you wire the bose into the speaker outputs instead of using the preouts, then usually the rear pre out can be changed to a sub one that can control a future additional sub. If you want to amp and replace all the speakers then 3 pre outs would be best.
Pull the headunit out and check all the wiring, its possible it use to have aftermarket speakers amp and in the haste of converting it back to bose they've missed a connection. The stock sat nav is stand alone so should work with the bose headunit also. My bet would be on the extra ground wire needed to turn the bose amp on, everyone always forget this.
It would require a custom fascia to get in the sat nav cubby hole. Best would most likely be replace the sat nav with the cubby box and replace the existing headunit with a double din sat nav unit.
That unit has 3 preouts, if using the preout method to hook upto the bose system 3 will give you more scope for the future but if people are wiring them directly to the speaker outputs then that leaves the preouts on the headunit free to control a seperate sub.
You cant directly feed the bose sub, the front and rear signal goes to the bose amp in the boot, this then sends a signal to the sub amp. I guess you could in theory do it but i dont know anyone who has. You'd need to work out what type of signal the bose sub amp takes, it could just be a low level signal.
You ideally want a headunit with 3 preouts so you can control the sub,front and rears independently. No need to go double din if you dont want, you can get some decent headunits with ipod,sd card,usb etc now for well under £200.
The bose sub does have some power, its the position that i dont like. I swapped out the headunit first and used my imprint processor and the bose sub had plenty of kick, it just felt wrong and was annoying that you felt it in your back all the time so it had to go.
The headunit is the first thing you should look to upgrade. Without it you'll struggle to get decent sound from the stock headunit without fancy external crossovers. You can save some money though and not bother reaplacing the rear speakers. Buy a decent active subwoofer and a 2 channel amp to power the fronts.