I'm gonna take a guess.Given your noises from the valve train on the exhaust side, and the looks of that round part, I would venture a guess that you have a failed hydraulic lifter on the exhaust side.I'm not sure what that L-shaped broken part is, but the thing that looks like a broken-in-half washer could be part of the internals of a hydraulic lifter.
I'm with you. Don't ride it and talk to the dealer. Bring the parts down, they might know what they are and be able to give you a better prognosis. If not, ask what the first move is and how much it's likely to cost. I do remember one poster saying that it was a remarkably short time it took hime to get the UCE engine out of the bike, on the bench, and have the piston and cylinder out. It's a simple engine, it comes apart fast.Scott
Here is a shot in the dark...But.....Scooterbob. Take a look at item 50, on page 22. Rocker shaft assembly.. ...see that piece on top? looks similar to what will has posted up on the left.http://www.royalenfieldlesite.com/spip/IMG/pdf/bullet_classic_c5.pdf