First off WELCOME!

This place is fabulous and I know you will get a lot of help here.
I will try to answer these the best I can.. there tons of people here with better knowledge than me..
Jersey week is a week in November where the Jersey schools has Thursday and Friday off for a teacher convention.. over the years many people take their kids off of school for the whole week and head on down to Disney.. thus.. jersey week.
If you get
free dining.. its just like the basic dining plan.. 1 quick service meal, 1 table service meal and 1 snack, per person, per day of your stay. The character meals can be used with that, it counts as a table meal.. some table service meals are 2 table credits.. not sure if the cinderella one is.. I have 2 boys so we never do it..
There are so many different codes and deals that float around that you just need to play around with them and see which one is the best for your family.
For me, I would prefer the buy 4 get 3 free. We are staying at Poly and it would save us probably close to $900.. That would work better for us than the free dining.. I have 2 boys who eat like little birds..

and would rather be riding all the rides than sitting down and eating, so if we had the choice, I would choose 4/3.. now don't get me wrong.. I would take the free dining!!
Not sure on the specials over Thanksgiving, but here is a link that shows you the past deals that have been offered.. when they were good for and the dates they were released
And I'm not really sure about a place to eat for Thanksgiving since I haven't been there during that time, but I'm sure someone here can help you out with that!