Thanks everyone for the replies.
I just wasn't certain because of the foil, the yellow cable, the red cable, and then the bare metal wire surrounding it.
Can you correct me if I'm wrong but.
1. The foil does not matter. I can just strip it away without a problem occurring, right. No interconnection needs to be made with the foil.
2. For the outer, bare metal wire, I just bundle it together and then solder it to some other cable/bundle? Is there any significance in it being on the outside, no insulation, and wrapped around the wires/tin foil? The extension cable can be insulated and not surrounding the cables underneath, right? This of course means that the bare metal wire is essential and not unnecessary.
3. For the red and yellow cables, as already mentioned, its just a connection to the other cables extension cables.
Just to emphasize, it is mainly the foil and outer bare wire that was confusing me. I should have made that more clear in my post.
And to answer your question, the fuse box and battery is in the trunk. I am mounting the dash cam in the front, and so it needs to go all the way to the back.
Thanks again.