ok, first thing first...
-Do I want to run a power wire from the battery to the head unit or is the power in the oem clip good enough? Same question for the ground? The Alpine wire looks so much thicker than the one to the stock radio.
you should be more than fine using the stock powerm and ground wire in the factory harness, but if you wanted to upgrade it, 10 awg works great, for both pwr, and ground.
-Do I need a cap? I have a 1998 2.2L Sonoma. I beleive the stock alternator is 100amps. Will doing the big 3 conversion be necesary?
I wouldn't waste any money on a cap. useless IMO. the stock Alt should be fine for the system you stated above, but if you wanted to upgrade something on the cheap, doing the "big 3" even without upgrading the Alt. would be a great idea, and it's cheap and easy to do yourself.
What's the best way to run power to the amps? I was thinking 4gauge to a distribution block mounted to the amp rack with a short 8 gauge to each amp. Do I need a distribution block with fuses (one for each amp)? I'll have a fuse on the 4gauge at the battery.
that is a perfectly fine idea. as far as fusing on the distro block, I wouldn't say it's stupid to go without them, as you have a fuse on the main 4 awg pwr wire, but if you can, then I would.
How do I do the remote turn on for 2 amps? Do I need a relay? How would the wire scheme work for that. Where would I get the power? I understand that the head unit would turn on the relay but what powering the other side?
And last, but not least, what you want to get, is a standard SPDT relay, you can get them at Canadian tire, NAPA, or any autoparts store, and wire it up like this:
then you will be able to connect as many things to that remote turn on lead as you wish... hope that helps
Mark