Minimum Summer Leave?

There is some magical number of days which if you have less of, you have to get TAC approval for, in order to go under. I think its around 2 weeks or so, but typically, if you want more than that, its possible as well as filling your summer up to the brim.

I had about 10 days off last week. Most of my classmates had closer to 3 weeks. Its all dependent on what you choose to do for your summer details.
When are cadets notified of their summer details.?

Typically, we would have found out February'ish. This year with sequestration, summer details didn't come out until the last week. Either way, you'll have plenty of time to work with your TAC to deconflict your summer and figure out what you want to do.
Is there a minimum guaranteed summer leave for cadets?

Anything lower than 14 days or higher than 31 requires approval. Cadets typically do 2 assignments every Summer so it will depend on the length of those. Most of the time, the leave is broken up into pieces but it is possible to end up with one big break.