When I've run numbers of hypothetical trips before, having an AP makes free dining not worth it because of the increased minimum ticket requirement (2 days per person). If you can get a discount on a room, general public discount or AP, adding an AP Dining Plan is probably cheaper than paying rack rate for a room, getting free dining, and paying for extra tickets you don't need.

So, I don't have the answer you're looking for. You could save them and use them on your next trip, but if you'll be renewing the AP you can't use the value of the ticket for your renewal.

And yes to your second question. It's actually good for 366 days and expires at the end of the date you bought it (a year later of course!).