Just to clarfiy --
Almost all the cheap brands make a big deal of peak/max power. It is a completely meaningless figure. They choose it virtually at random. Its only purpose is to look impressive to people that don't realize it doesn't mean anything.
The AC4000.1d (if that's your amp) is roughly 1000w rms at 1 ohm.
Don't know exactly what your 4 ch is. The R1100M is a mono amp and I don't see a 4 ch Boss with a similar model #. The R2504 that they call 1000w has a pair of 25A fuses and is likely around 75-100w x 4.
So what you're working with is a ~1400w system.
I'm guessing your Mustang has a 130A alt.
This setup would run fairly well on the stock electrical system although upgrading the factory wires wouldn't be a bad idea.
H/O alt certainly won't hurt anything and will give you a lot of room for amp improvements in the future.
You don't need 1/0 for the 4 ch. 8 awg would work fine. But again, if you're going to upgrade - big wires now is a good thing. It will be tricky getting 1/0 connected to an amp with terminals intended for 8 awg.