To identify your grape record when it flowers, when there are immature  grapes, the color of the grapes when ripe, when the grapes are ripe, thickness of skins, size of fruit and how they taste: sweet, tart, musky, robust, then check your list against the varieties that are hardy in MN.
http://www.extension.umn.edu/garden/yard-garden/landscaping/minnesota-hardy/
http://www.extension.umn.edu/garden/yard-garden/fruit/growing-grapes-for-home-use/

Check out the references for how to care for your grapes and be on the lookout for the latest pest the 
Spotted Winged Drosophila. 

Thanks for the links to the websites. Is there someone who could examine the photos below and offer some advice/input?

Different grape varieties look similar but often taste different. You might take some to a MN vineyard and see if they can help you. There is no one in extension who does variety identification.

Those look luscious, by the way.