Dealing with the melted wiring in my car was the first major project I had to tackle. Back story here:
https://e9coupe.com/forum/threads/rear-light-dilemma.42792/post-375463. I would just repair the problem areas, with the following caveats:
First off, you need to know that when a circuit is overloaded, the heat arising from the resistance overload occurs at both ends of each and every effected wire. For example, if you find a melted light socket (which I did), you will find a melted wire where it connects to the light, and another at the other end of the curcuit, in my case at the fuse block. You need to check both ends of the wire to ensure you are repairing the entire problem.
An exception to this can occur if wiring insulation is damaged because a wire becomes grounded. Then you have three locations to check - one at the unexpected ground in addition to the other two ends of the circuit.
Second, when replacing melted wires, find wiring of the same color, and unwrap the wiring harness back to an area where it runs straight and is not near a grommet or terminal. This is so the splice is not stressed once you are done. To get the replacement wire and terminal, I have another wiring harness that I canibalized, so I obtained connectors and wiring from that old harness. (I believe connectors are available. I saved this site, but have never bought anything from them:
https://www.rdae.nl/4805-mm-3-2926.html.) I use crimp and solder connections with a small slit in the middle to allow solder to flow onto both wires after they are crimped into the connector (like these:
https://www.digikey.com/en/products/detail/panduit-corp/BS18-M/447759), with shrink wrap over the connection, and then retape the harness (usually over the old tape). That said, most people will argue that a properly crimped connection is sufficient.
Third, you mention missing insulation on existing wires. This is an entirely separate problem than those I encountered, and indicates wiring is not properly routed, or alternatively, not properly protected in areas where it crosses through the firewall or other bulkheads. Here you need to address not only the wires, but you also need to consider routing and whether that is done incorrectly and the need for grommets (which are probably missing). In general, wiring should have very little room to move. Secure loose wires with zip ties.
