If your original reservation is for a package, then there's no problem in adding the Dining Plan to your reservation at any time up to about 10 days before your trip. If you're outside the 45-day window for your trip, then your balance due is just increased by the price of the DDP. If you're within the 45-day window, you'll need to pay for the entire cost of the Dining Plan immediately upon adding it. (Your package should have been paid off by that point, so only the added costs are due) And because you're adding to the total price of your package, Disney will waive the change fee normally associated with making changes inside 45 days.
If your reservation is a Room Only reservation, it gets a bit trickier. The Dining Plan must be part of a package reservation that includes hotel and tickets (unless you're booking as an Annual Passholder, which eliminates the need for tickets).
If you have a Room Only reservation, I believe that you have to cancel your existing reservation, and then book a new Package. The problem is that the money from the Room Only reservation can't be credited to the new Package. It has to be refunded back to you. And because you'd need to pay for the new Package right away, you could have double the money for the trip tied up for a week or two...
As for booking restaurant reservations (ADRs), they are independent of your hotel reservations. Anyone can make them, you don't have to be staying onsite or have the Dining Plan.
The only time that a Disney hotel reservation is required is if you want to use the "90+10" booking feature, where you can call and make ADRs for your entire trip (up to 10 days) in one call on the 90-day mark from your arrival date.
Otherwise, those without a Disney hotel reservations (or if you'll be staying at a Disney hotel and haven't booked it yet) would have to call back at the 90-day mark from each date they wanted to make dining reservations for.
-Rob
