Is reddish wire in a copper cable?

I assume that it is copper and I would also like to know how to solder such a cable (Ldekabel from the laptop / cable break) again, or if that is even possible (have never soldered anything in my life).

Yes. Copper can be soldered very well. But you can also twist the cables and then insulator (zB adhesive tape) drum. Is less pretty, but goes faster.

Not necessarily.

Actually, every cable can get a reddish color when too much current flows through it.

It's copper and it's easy to solder if you can.