You should listen to me. No, seriously, listen to me.
Join Date: Oct 2008
Location: Santa Barbara
Motorcycle: Blue 2006 GSX-R1000
Re: Please recommend what Stator and Rectifier to buy
IMO you're playing with fire to be using a stator with "serious black burns on the copper wires inside". That generally means that there's some internal shorting, which is not good for the rest of the charging system.
"Do the copper wires overheat because of the engine temp and how to solve this issue?" On the 1000's, and presumably also the others, oil is sprayed through the holes in the rotor to cool the stator. There ought to be a large ENGINE LUBRICATION SYSTEM diagram in your service manual that shows as much.
The contacts normally fail from corrosion. Once they start to go bad, the contact resistance goes up and resistive heating makes things worse. Eastern Beaver sells a sealed connector specifically intended to replace the unsealed OEM connector. Dielectric grease might help a brand new connector but cleaning contacts is generally a waste of time. My mindset is to plug the halves together when new and then not touch it. Replace both sides, not just one.
There's also Race Tech Electric but they're also not in Europe. I'll bet that someone in the UK/Europe does it but I don't know who.