You can use female Quick Connects
* which crimp onto the wire, or you can solder wires directly to the contacts. If you solder I recommend insulating with heat-shrink tubing and if you use quick-connects, I resommend the insulated type.
You can get quick-connects at from places that sell electrical ro electronic parts, hardware stores, home improvement stores, or auto parts stores. There are a couple of popular sizes, so make sure you get the right one.
Also I'm assuming the ground wire skips the relay altogether and goes right across from the C14 ground pin to the 13A ground pin? What about neutral?
The ground & neutral are connected directly. The hot wire is switched through the relay. If you have a double-pole mechanical relay, there's no harm in switching the neutral also, but the ground should be "permanently" connected.
In order for current flow, you need a complete circuit. You can "break" the circuit and turn-off power with a switch in either
the hot or neutral side. But for safety reasons, the switch/relay normally cuts the hot connection.
* "Quick-connect" or "Quick disonnect" mioght be Americqan slang/jargon, and they might have a different proper name..
This is a Spade Terminal
and this is a Ring Terminal