Hi,
I assume u only took the largest cover off. If u took off the small chain sprocket, please reassembly, as to Ronzworld's preceding post.
With the clutch hand lever RELEASED, the wire of the cable should be without slack, the "plate" should feel firm (not loose) and even (not uneven) and the rear wheel should feel locked. If u can turn it hard enough (by hard or pedalling) u should hear the engine a bit (you'll know).
The clutch hand lever may be a little hard at first. When u fully squeeze it in, the plate should become slightly loose (and stay loose if u lock the clutch hand lever with the little pin).
You said, "I noticed with the cover off that the plate, when it is moving outward, doesn't move evenly. Is this normal? ". Yes, it becomes slightly "loose"/separated when u squeeze the clutch.
If u get someone to help u squeeze the clutch hand lever (or lock it with the pin), u should be able to push/ ride the bike around (it may be slightly harder now than before).
Otherwise the clutch is not correctly adjusted or there is some other fault.
"No spark": have u tested this? Please let us know how u go. Maybe a picture of the clutch lever on the ENGINE (u might have to put it in your photo album if it's big). It's awesome when u hear the first cough! Please stay safe!
These issues can be difficult for all involved if there is no resolution.