The diode and the relay question
The damage you are thinking of is due to the voltage spike caused by the inductance of the relay coil when it is turned off (V=L*dI/dt).  Since the relays are part of a complete package and the coils are controlled by a wireless receiver, that issue does not apply to you.  You can even see one of the protective diodes in the picture of the relay module, it's the little horizontal black cylinder with silver at one end, between the capacitors (big silver-topped cylinders) and relays (blue boxes).

However, I don't think that relay module is appropriate for your purposes because it is labelled as "momentary", which means the relay (and therefore your receptacle) will be on only while you hold down the radio button.

You could, however, use the momentary relays to turn an additional latching relay on and off.  I'll leave you to google up schematics for doing a latching relay.