Nancy,
Advanced Dining Reservations (or "ADR"s as you mention) do not require that you have park tickets, a dining plan package, nor hotel/resort reservations. They are almost 100% independent*.
The only requirement for making an ADR is that you are within 180 days of the date you wish to make your ADR.
* I say "almost" because:
1) When you have a package that includes one of the Disney Dining plans, you should add this information to your ADR before you arrive at WDW. Nevertheless, there is no problem making your ADRs first, and then adding the information that you are on the Dining Plan at a later date.
2) If you have a resort reservation, you get an additional benefit of being able to reserve up to the first 10 days of ADRs once you are 180 days from the first day of your resort stay. See
here for more details on this perk.
Please be aware that the time of your ADR does not mean that a table will be immediately available at that exact time. You should plan to arrive 5 minutes prior to your ADR time, and your party will be seated at the next available table for a party of your size (usually only a short wait, and rarely more than 15-20 minutes). I mention this because I met a couple at WDW last weekend that was very upset that their table wasn't available exactly at their reservation time. They said they were so angry that they left and decided to eat elsewhere. I felt bad that their expectations weren't met, but I also felt bad that their expectations weren't very well informed. So I mention this in the hopes of helping more people have more appropriate expectations.
See
here for more Disney Dining FAQs.