Yes, the activities schedule is posted a week ahead much of the year, though sometimes they do a month-long calendar.
Nunzio's is one of my favorite spots. I grimace when I say this because inevitably someone will disagree on some level, but it appears to be "authentic" recipes there for things such as Bolognese and their pasta of the day selections. I'm fully aware that people who come from the NY/NJ, etc., have particular ideas of authenticity. But, that's true of any regional food. As a general rule, I've found in my far-reaching travels that as long as you stick to those places which offer a good menu from someone with true knowledge of the cuisine, you're okay, and Nunzio's has that. In this case, according to their website, the family moved here from the Puglia region of Italy (and I've long admired wines from that terroir), so they brought along their recipes.
On a bit of a side note, I've also often found the argument that something isn't authentic because it's not made the way "I was taught" or "where I grew up" is a bit tiresome. I hail from the South originally, and I can tell you that the way we made cornbread and collards was definitely authentic...but also different than a style you could get just across the Louisiana border not 25 miles away. I simply love the variety. While you don't appear to be there long, next time you travel back to HHI, I would also recommend OMBRA Cucina--Chef Michael Cirafesi hails from NYC originally and has been voted top chef at HHI many years.
Yes, you will find something to enjoy at the resort, even if it's just taking in the late night sounds and smells. There is something almost magical about that resort. As for a restaurant, I doubt that will ever happen. The most accepted (and likely true) story is that when Disney approached the city council about building the resort, the council wouldn't approve of the permit if a restaurant was built as, at the time, they didn't want to take away from the local eateries. Now, that the island is more of a year-round destination, that likely is less of an issue, but I still don't think Disney would ever be encouraged to put something in. At any rate, enjoy your trip!