Things have just taken a downhill turn at the bars, unfortunately. We still haven't re-checked out some of our favorites, but that's in the near future.
The appetizer and drink menus have just been overhauled at the bars to apparently reduce the amount of people eating at the bars as opposed to the restaurants. The food quality seems to have been reduced as well. However, I'd still check the bars out for the great drinks and yes, less of a family atmosphere.
You'll want to stick to bars that aren't right near restaurant entrances. Some of our favorites for that are Victoria Falls (AKL), Territory Lounge (WL, right near a restaurant entrance, but it always tends to be quiet), Matsunoma Lounge in Japan at Epcot.
At the bars, you can just walk in, first come first serve. At the Matsunoma Lounge, you do have to put your name down on a list.
I don't know about a bar at Fulton's, that's something we haven't done.
Yes, you'll just have appetizers to choose from, but usually they're pretty substantial.
No, you can't use the dining plan in the bars.