The wires may not be copper, or the strands may be individually insulated, those wires can be a pain and I'm not sure what do do about that, I suppose you could try crimping on a more easily soldered wire.
For the connectors a trick I use is stuff a piece of wet paper towel or cotton ball in the end around the pins, or if the connector design makes that impractical, support it so the end of the connector is submerged in container of water. That will keep the pins cool enough to not melt the plastic, and the thermal conductivity should be low enough that you can still heat up the end you need to solder.