dining plan is not related to park tickets or days you spend in the parks at all. The dining plan is tied directly to the number of NIGHTS you're staying, so you will have 7 of everything on your plan, per person. If you're on the regular "plus dining" you'll have 7 counter service, 7 table service and 7 snacks per person age 3 & up in your room. (plus each person gets a refillable resort mug, too.)
You can begin using your dining plan credits as soon as you check in (even before room is ready) and you can continue using any remaining credits, if you have any left, until midnight on your check-out day. So you can stretch your credits out over the full 8 days...or use them up sooner if you choose.
How many days worth you bought on your tickets...who knows? You need to check your reservation to see if you bought a 7 day ticket or an 8 day ticket. If you want 8 days, it would not cost much to add the 8th day...at that point it's down to about $5 or $6 more to add day 8 to a 7 day ticket.