I'm hooking up my connex4600 turbo to batteries

#8 wire for a 40 amp breaker is fine for what you have. You could put a 45 in if you wanted to and #8 wire would still be fine.

First of all, what size fuse? Check the amp and see what max amperage is, and insure your fuse is that size. Secondly, I suspect either a blown speaker or blown outputs. Disconnect the speakers from the amp and see if the fuse still blows. If it does, either you are hooking two wires up improperly, or your outputs are toast.

Depends on how long the run is. Remember the fuse protects the wire not the load :-). Average run is 15ft, most run a 50amp, or 40amp.

hook power wire to positive side of baterry then to amp power fuse needs to be no more than 18 inches from battery fuse size differs due to wire size ground wire needs to be same size as power wire p.s. hook up ground & power wire before installing fuse hope i was helpful

with no signal input the fuse should not blow ,if it blows then the amp has a short on it ,if it blows when the volume is turned up really high the try 60 amps .

All amps are basicly the same. It should be plain as day where the speakers connect to.
The 12V screw connects to the main power from battery, be sure to fuse that wire and use a proper size wire, thicker is better,I suggest at least 8gauge with 40amp fuse. The GND is ground and should connect to car metal, file paint for soild connection. The REM is remote and connects to the remote of headunit or if you have a stock deck to the acc of car found in wire harness of headunit. Plug in the RCA's to head unit, or get a converter to plug into speaker wires from car if you have a stock headunit.

this kind of problems usually happen when the amp is not getting enough current to power up the  
 amp. the moment a loud low frequency hits the amp it fails. cud be ur power unit not giving enough power to the amp or u have a loose connection somewhere on ur power line. besides 8gauge is a bit small. try using about 4gauge. should have good ground too. they draw large current so ur battery should be in top condition as well. 

Your best bet is to buy a cap. A capacitor is an external battery booster like device. It boost power to amp. The thicker the wire the better. Power and ground. Shorter thicker ground wire the better. Make sure it is not on a painted surface. Scrape down to metal surface!!!!

You normally have to drill a 1/2" hole depending on the size of your wire though the firewall and down the pillar then under the rocker panel by the bottom of the door (where you step in/out) and then on the side of the back seat to the trunk. Expect about 20-30min to run the wire. make sure you use a rubber/plastic gormmet on the firewall to keep the wire from shorting out and you need to fuse this wire off the battery. use the same amp fuse as your amp. (if 60 then use 60 at the battery)

bigger is better, recommend 4 gauge. 50-60 amp fuse