Yes, public tickets go on sale usually in mid June, and I'd all but guarantee that Pitt will have some availability once tickets go on sale. Usually someone posts about the public ticket sales under General Team info or something similar. It'll be common knowledge once they announce the official date.
I'll let others speak to it but Mishawaka is just a regular old town, places to eat, drink and there's a mall. Idk what you're looking for, but I'd prioritize sight seeing on campus on Friday over Saturday; Saturday will be an absolute zoo.
We actually just went to Crooked Ewe Brewery & Ale House during the Spring Game a couple of weekends ago and enjoyed it. Pretty busy though, and that wasn't even a game weekend.
Can't really speak to the last one, I've seen plenty of Lake Michigan and the Great Lakes are beautiful, but I've never done it in the Michiana area.