Nate - if the EOS is a "normally closed" switch, it needs to stay closed until the very end of the stroke. So when you're holding the flipper button down and the bat is up, there should be an 1/8" gap between the two contacts. From a glance it looks like if you pushed the plunger into the coil the EOS would engage way too early, cutting the high power and engaging the much lower "hold" power, resulting in ultra meager flips. Also, the EOS is the one closest to the coil. I'm pretty sure the one on the "outside" of the stack is the lane change switch.
The extra spring is there in case you wanted to convert the return spring to the later WPC style shown below. It's a slightly better return spring than the big one that fits over the plunger, but requires that you drill a hole in the bracket that is holding the EOS -
The round thing is a spring washer that fits between the coil and the bracket that holds the coil in place. You only really need this if you can wiggle the coil back and forth when you've attached the coil stop.