You do not need a ticket to add the dining plan if you are staying on a points reservation. Just add it to your reservation through MS at least 48 hours prior to the trip. You will then pay at check in (at least for the time being--that is changing in the fall).
You are given the DDP credits per night, so for each person, you will have 1 TS, 1 CS, and 1 snack.
They are good until midnight your check out day. So, you can use them in any way that you want. You can use them all the day you check in or save some, as PP mentioned, on your check out day as well.