Yes. The Shooting Gallery is right next to the Advance Shop in Lynna Village (in the past). Its the door on the left.
It is a reward. If you buy the one in the shop, then you will end up with Dimitri. The event takes place after Level 3, and before you go to the Nuun Highlands. At this...
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For Ricky and Dimitry, you have to get their flutes prior to the event after Symmetry City with the fairies from the woods. I end up with Moosh most of the time because I never go and get one of the other Strange Flutes. Here is a link to a page at Zelda Wiki that...