The dining plan makes absolutely no difference when booking reservations UNLESS you want to avoid prepayment on CRT or a dinner show (meaning you will be paying on arrival with dining credits instead of paying for the entire meal for your full party at the time you book the reservation). To book CRT or a dinner show online and have any hope of it turning out without your being charged in full, you will need the confirmation number for your DVC rental reservation. If you don't already have that, you can get it from the member you are renting from. Then when you click the 'I want to use the dining plan to book reservations" it will ask you to input that number.
Without the number, you will need to pay in full for CRT or a dinner show and then change your payment upon arrival to dining credits and have the full payment refunded. If the system accepts the number and recognizes that you are on a reservation with the dining plan added, then you will be asked for a credit card number just to hold the reservation. Always check closely before you click any acceptance and make sure you are not paying in full at booking. If you are being charged in full by the online system you may have to call.
For any other reservation, it makes no difference at all at the booking stage whether you are on a dining plan or not.
If you want to book 180 + 10 at your 180 day mark, you will also need the resort reservation number from your DVC member. But that is to confirm that you are staying at a Disney resort and are eligible for 180 + 10 booking - not anything to do with the dining plan.