That's another point, you need a big enough alternator to run your vehicle and your amp. Your stock car alternator was designed to run your vehicles electrical components with amperage to spare.
If you have an alternator less than 100 amps, I would get a higher amperage alternator.
Your coax cable should have some printing on every foot of cable or so telling you what type of cable it is. If it a clear cable, it is kind of hard to read but look carefully and it should be there.
RG8X is good enough for what your are using for. If it is RG58 I would replace it.
Get an minimum 100 amp fuse and fuse both positive and negative leads ( negative leads carry voltage too) and go direct to the battery with both leads. This can prevent ground loops from appearing which can cause havoc on your radio and vehicles electronics. I experienced ground loops before with one of my mobile installs and this cured it.
Car stereo dealers sell the inline plastic bubble fuses for wire gauges up to 2AWG and I have seen them at Autozone too. Number 4 AWG is more than adequate for your mobile install since I doubt it will be more than 10 feet.