How to connect C14 and UK AC mains to relay?

Combo:
I was planning to solder a wire to each pin and then screw them into the appropriate connection on the relay -- is that ok?

Yes, but see below.

After a lot of googling I see they look like "spade terminals" -- is that what they are? If so do I need to order the right size female terminal (what size would that be?)

Measure the width of the terminal. The standard sizes are 3/16", 1/4" and 3/8". There are also some larger sizes but these are rare. Halfords sell insulated spade connectors in those sizes.

and "crimp" it to wire?

Yes. Or you could use uninsulated ones and solder the wires in place with some heat-shrink over the connection.

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?

Connect that directly too. Only switch (with the relay) the live wire.