I do not know how difficult it is to get in. It is fairly popular, but less busy, I believe than the Cafe downstairs. If it is not covered by the dining plan, you have a good chance. If it is, call early.
Yes, you call the same number 407-WDW-DINE. Be sure to tell them that you want the Dining Room. And say "upstairs". Some CMs get them confused very occassionally.
Ted