Jumper cable connector melting

Huh, that makes sense, thanks!
I hadn't thought of that and I recently had the power go out in the block and, normally my PC is on 24/7, but I had to go to work before the power was restored so when the power got back the PSU side had power, but my PC was off (I'm not sure if that particular USB port provides power while PC is off but I imagine it doesn't).

If I were to make the suggested modifications would the whole thing be ok in such a scenario? My guess is the resistor is to prevent the parasitic powering so the answer would be yes?

Afaik resistors don't have anything special, just how much Ohm of resistance they provide, but I'm not sure about capacitors - do I just search for a 1000uF capacitor or is there something else I need to look out for? Do they differ by voltage or something?
Also, the capacitor is connected in parallel to the PSU/LED strip?

If I add a resistor and capacitor I'm gonna have to add a board to the circuit, I can't really have them floating around unprotected. What's the best option, one of those square circuit boards to solder the components onto and then when I solder the things together what's the best way of protecting the thing? Or is it fine if it's just tucked away behind the TV?

Final question, while I'll replace the melted jumper cable, do I need to replace the Arudino? Or maybe just write off pin 6 and use some other pin instead? (don't know if there was/could have been any damage and to what exactly).

Thank you so much, I don't know why but I can program pretty much anything, but when I try doing anything with electricity I'm as dumb as bag of rocks :-[