Have a great trip!
If your tickets are OLD ENOUGH, then you can use them. They must be before the current "Magic Your Way" ticket era, or, have had the "no expiration" option added.
Assuming that they are old....
If you have enough days left on your old tickets, it will be MUCH cheaper to just use them as is, rather than trade them in. Since they've been used, they will give you a fairly small amount for a trade-in. (I believe that if they were 5 day PHs and you used 3-days previously, you will get the value of the cost difference between a 3-day and a 5-day pass at the time you purchased them. In other words, less than the cost of a single day now.)
If your trip will be short enough to just use the old tickets--great! If you need to buy more tickets consider what your future disney plans will be. If you usually go for 2-3 day trips, you'll save money by purchasing a 10-day, no expiry ticket and saving it for the future. If you are going now for a full week and only have 2-3 days on your old passes, you'll save money by buy a week-long ticket now and saving the old ones for some time when you come for a shorter trip. Etc.
As for the restaurants and parks on NYE...
Call WDW-DINE as soon as possible. My guess is that there will be something still available (or available because somebody canceled) but whether or not it will be something you want is a different story. You may wish to eat a counter service meal on NYE and a nice meal out the next evening (when the demand decreases significantly).
Where are you staying? If you are staying on disney property then you can probably get in fairly late. They don't close the parks at a specific time, but, rather at a particular occupancy. As occupancy grows they first close the parks to guests who are not staying at a disney resort. Then, much later, they close the parks to on-site guests.
Last year, we arrived at disney around 4 pm on NYE. We checked in at ASMusic, went for a swim, ate dinner at the CS at ASMovies and then called disney info to check on the status (probably around 8pm) of the parks. They told me that all parking lots, except for the TTC, were full and that two of the parks were closed to off-site guests. I remember that the MK was one of them.
I have also heard of years where all parks were closed to outside guests as early as 10am.
So, if you weren't planning to stay on-site and you are picky about which park you visit, you may wish to look into an on-site accommodation.