Which exact model of the extender do you have? The original is Z wave classic, the newest one is Z wave plus. The zwave plus version will have much longer range.
Neither is necessary, since with the current versions of zwave and even going back a generation, any mains powered Z wave device will act as a repeater. A Z wave plus pocket socket or light switch Will do much more for your mesh then the single purpose extender classic device.
There shouldn’t be any difference between a hardwired switch and plug in pocket socket as far as their capabilities as a repeater, so I don’t think you have to worry about that. The most important thing is to add one or 2 z wave plus mains powered devices and then run the Z wave repair utility after they are in their desired locations.
Have you had a chance to look at the FAQ on zwave repair messages? I don’t think you’ll do anything different after reading it, but it might give you a better idea of what you’re looking at.