Extending extruder heater and thermistor wires
Soldering is fine, both for the thermistor wires as for the heater.

The wires don't need to be particularly special, though there are some things you should keep in mind:


Current. The heater can draw up to 3-4A, the wires need to be able to handle this. The wires for the thermistor can be thinner.
Flexibility. The hotend (presumably) moves, so the wires should be able to withstand frequent movement. Use stranded (rather than solid) wire.