Yes, IF the rules of proper splicing are followed, dissimilar metals can be successfully spliced.
Some of those rules that I can recall at the moment include:
Yes; it is tinned copper.
It is traditional to use the copper colored wire as the positive. Of course, the electrons don't care what color the wire is as long as you hook it up the same at both ends!
Speaker cable can have an insulator that could be any color. The wire inside is typically silver, copper or gold colored.
Whichever one you connect to the positive terminal. The colors are there so you can find the same wire at the other end.
When you place copper wire in a silver nitrate solution, your result should be a heterogeneous mixture.
The price of copper today is $3.43 a pound. The price of silver today is $12.90 an ounce. Copper is much cheaper.
The copper and silver will combust.
My PC speaker cables have a copper wire, as well as a insulated (white) copper wire. The headphones (Sony) appear to have 3 wires in them - green, red, and orange. The links you posted are more for car/home theater speaker wire.
Couple options. Strip off a half inch of insulation of the wire were the wire is separated. The splice the wires together. Apply electrical tape to the area that the wires were spliced. Or, replace the whole wire. I recommend replacement.
The best conductor of electricity is copper wire. Silver is a better conductor than copper, look up basic data. But silver is not practicable for widespread use, copper is nearly as good and more practicable for engineering use as well as cost.
It doesn't really matter, as long as you connect them to the same polarity at both ends. Most people use the gold or reddish-copper wire as the positive, as it is the red terminal and the silver, or non-colored lead to the negative as it is black.
Black wire to copper screw, white wire to silver screw, bare copper ground wire to green ground screw.