well guess you can fix both problems at once while you have the clutch cover off. Coolant is probably getting in to your transmission through the water pump seal. The water pump is in the clutch cover so you can fix that probem on the bench after you take the cover off. Now would be a good time to upgrade to a Pro Design Billit water pump impeller and shaft. I would do New berring, seal, pro design water pump impeller, and proabably even a new plastic gear while I was in there.
As for the kick starter not working I bet the Idler gear bushing is shot and it wabled off the shaft. You can get a new bushing washer and E clip from FAST instead of buying the whole gear from yamaha. He would aso have your water pump parts as well.