That coil looks to be a slingshot kicker coil. That is a direct coil, that is, it's not CPU controlled. What controls is is the top side playfield switches, which complete coil power (30v) to that coil. So yes, it can fry pretty easily if the top side playfield switches get bent too close. It's probably an a5195 coil which should be about 3 ohms. and yes it should have a diode 1n4004, with the non-banded coil lug side of the diode connecting to the green wire. Technically a 1n4001 diode would work (as the backlash voltage is about twice coil voltage, that is 30*2, which is under the 100v 1n4001 threshold.) But there's really no reason not to use the 1n4004 (400v) diode as it's the same price.