The rectangular symbol represents the relay coil..Some small relays come with the diode as part of the package, most don't.
Negative spike supression ??
A reverse diode will give you adequate supression, a resistor will add current draw to your output , it will be an additional load..
Diode check :Meter in diode check(arrowhead) place leads across diode, reading will either be open (ol) or show small voltage(voltage level varies from type to type,typically .7v) Reverse leads on the diode and you should get opposite of first reading..Reading open in both directions indicates open diode (no current flow) and a voltage in both directions indicates shorted diode (current flows both directions). Most of the time you can check diode in circuit, if you get a questionable reading, disconnect one lead of the diode from circuit and check again. Checking a diode in the relay coil circuit will give false readings since the coil acts as a conductor that is parallel with diode..
Hope this helps..