Yes, you can use the system without eyes. Simply don't plug the eyes in. And yes, the E1 also comes with eyes. However, the E2 has support for break-beam eyes where the E1 only has support for bounce-beam eyes.
They sense whether there is a ball sat in the breech. If they don't sense a ball, the gun won't fire (or fire at a hugely reduced rate, to eliminate chops) It's there to stop (Hah!) ball's being chopped in the breech. Not really nescesarry on a well set-up cocker though.
The timing rod goes, the 3-way goes and the trigger frame goes. The frame is replaced by the E2 frame, the 3-way is replaced by the solenoid, and the connection between the two is now electronic instead of via a timing rod.
The E2 kit comes with everything needed to fit it to a standard autococker, except a way of mounting the (optional) eyes.
The E1/2 frame will fit vertually every cocker on the market apart from the Trilogy (i think) as its front pnu's dont create enough room for the new noid, ram and LPR.