Call the John Deere house in your area...they will know this...most John Deere Dealers only work on John Deere., and in my area, we don't have those..Texas...but, any John Deere House will be able to tell you...I can work on the engines...anything el...
John Deere is not the company they used to be. I doubt they have a tensioner and if there is it has little, little adjustment. If the belt keeps breaking clean you better bring it in for some warranty work. If it shreds everytime your working it too ...
If its sat for a while, before running it you shouldve gone over it, tune up, oil change, fuel filter - so you wont have to do this all later. With the deck vibration, it sounds like somethings either loose or sticking - did you check the deck out be...