[SMAN]'s correct about the power cables...
here's a link to a page that should clear up a few points on amplifier installation.
what u're experiencing witht he buzz is called alternator noise. Basically, the magnetic field generated by the power supply wires have induced a voltage in either the signal or the speaker wires.
Separation is the key...
here's another link to a page that might be of some use.
About ur amps cutting off, ensure that the power wires are connected to the battery terminals and NOT the accessory wires. Most power amplifiers have '+ve', '-ve' and '+12V REM'. +ve and -ve connect to the battery terminals and the 'REM' connects to the accessory wire so that ur amps only work with the key in the ACC ON position as a protective measure.