Check the motor mount bolts. They will work loose even sometimes just an 1/8 of a turn which will allow the engine to shake mostly at start up and shut down, but sometimes when the pto is engaged.
• In my part of the country, Ethanol fuel can go "bad" in as little as 8 weeks. Especially if the vehicle is left stationary. The mere fact that you asked makes me extremely uneasy. If you have doubts, then change it.
• Lots of things can cause the engine to knock. Start with tightening every nut and bolt on the mower. When was the last oil change ? When was the last grease job ? How old are the belts ? Any broken pieces of belt flapping around under the covers ?
