I wouldn't wrap the capacitor lead under the cap because it may contact one of the leafs of the EOS switch. Depending on how you wired the switch, that might cause the EOS switch to always be "closed", which will eventually burn up your coil.

You might be interested in a video I posted that documents the weak flipper issue and the fix...on a Cyclone, even!

True with the electrolytics you'll find elsewhere in pinball machines, but these particular types of capacitors are non-polarized. Doesn't matter which way you install them.

Your spring seems like it might bind up as it is now. Lots of rebuild kits come with a retaining bracket with little tabs that hold that spring in place. Without those, you have to rely on the coil sleeve protruding from the coil to center the spring. I don't see either in your second picture. There's some discussion here:
http://www.pinballnews.com/learn/flippers/index2.html