First off, no need to apologize for your handwriting; it's incredibly easy to read.
Here are my thoughts/questions:
1) I personally don't see a point in fusing your remote wire and I have never seen a recommendation to do so. I think that will only add more cost and complexity.
2) Why use a powered sub rather than using the sub channel of your Alpine amp? If you haven't already purchased the powered sub, I would put that money towards a MTX Thunderform enclosure. I had one in a 2004 F150 supercrew and it fit beautifully. I found mine on
ebay for a decent price. Not sure what year or configuration your pickup is, but it worked well for me.
3) Fuses are meant to protect the wire and your vehicle, not the amp. Look up the maximum current rating of your wires and fuse accordingly. Look at the size of the fuse element verses the size of your wire and this should make sense. If your amp is drawing more than it is designed to draw, then the amp is already malfunctioning or doing more than it is intended to do.
4) I'm not familiar with the pin numbers on the relay you included. If you can provide a pin-out or a part number for the relay I can give your a more definitive answer. I don't need to insult your intelligence by explaining how a relay works.
5) No idea why guys on their high-horses feel the need to insult you (or anyone) for asking car audio questions on a car audio site.
- Joe