the sprocket wiggle & sounds like you have wear on the sprocket hub is egged out(or your axle's splines are worn away) .
The clutch sounds like the pull arm is not in the correct position, check the clutch arm, you're prob'ly going to have to take it off the splined shaft & turn it a little - my 350X was doing the same thing & it was because the clutch arm was in the wrong position, I.E., it was kind of "in gear" with the clutch pulled in, & in neutral when released.
Good luck & let us know what you come up with.
Baltimore---Charm City, or Harm City? Ask Pat.....