50 Amp fuse by the battery is fine.
Although not an exact calculation, the general rule of thumb we use when installing is to add up all of the fuses on the amplifiers, and go for the next preferred value up. For instance if your amp has 2x20A fuses, that would make a total load of 40A, and the next preferred value up would be 50A. This means that everything can run flat out without an excessive main fuse. keeping the main fuse as close to the power source (battery) is critical for protection, and that cannot be stressed enough.
If only running the amp at low levels, then 8 gauge cable is ok (ish) although I would have preferred to see a heftier 4 gauge cable there.
At near 500 Watts, the Alpine amp is a good and powerfull choice, especially being a 4 channel, and it would be good to have an adequate power supply should you wish to use the full potential of it.
With the 8 gauge cable, the demand on power will be more than the cable can supply and over the 6 meters or so between the amp and the battery you will suffer from some voltage drop. You may find that if you crank the amp up, that it starts to cut out or distort at high volumes - at first it will appear that the amp is simply tripping out, but the switch mode power supply inside can only take that for so long before it goes bang. Distortion on a high quality amp is a very bad thing, and can always be solved!
For anyone else reading here, to understand and check for voltage drop, if you have a digital voltmeter, check the voltage at the battery, and check the voltage across the power terminals of the amp when running. It should be EXACTLY the same, but if you have even the slightest of differences, the gauge of the cable is most likely to be the cause of it, and needs to be increased in size.