Yes........
Yes, ........if your going to store any 2 cycle engine, it is highly recommended that you use a fuel stabilizer. Especially with the DI models.
Over time, fuel will become "gummie" or even harden like a "lacquer". If your only setting up for a few weeks, to even no more than a month, I wouldn't worry about it. But the engine should see at least 1 hour of running per month.