It looks more like a Lilly of some type.

I grow garlic, and the branching pattern on that doesn't look like any garlic I know. The garlic I've seen, all the leaves pretty much branch straight upward, not out at a 45 degree angle.

If it is garlic, though, you generally harvest garlic later on in the summer, maybe late June at the earliest, more likely August or so.

Then you save however many individual cloves back as garlic heads you want to harvest next year. Each separate clove grows into a new head. And you'll plant garlic cloves in late fall. I usually plant in October or November. Just get it in when it's cold out, but the ground isn't frozen. I haven't tried planting in pots like that for overwintering, I'd think they'd get too cold. We had a rather brutal winter this year, and all the garlic in my raised bed was killed off, and only about 2/3 or so of the garlic in-ground survived. I'll be covering it with straw this coming winter, assuming that it will be as brutally cold again.

Yes it is edible, it is the commonest source for commercial growers.

Harvest when the leaves die back and you have only 5 or so leaves alive.

Heck out this page http://thehousingforum.com/how-do-you-plant-garlic/