Probably. Since the box was introduced in the pilot and the Mane 6 finding their keys has been a story arc for the season, it will likely be concluded as part of what appears to be a two-part finale, as episode 24 will involve the Equestria Games.
Yes, the Season 4 finale of your Little Pony Friendship is Magic will be a two partner.
Yes, the official synopsis of the Season 4 Finale hints at the "Rainbow Kingdom".
It is not known what these flashes of rainbow in the pony's eyes is supposed to represent, but this will likely be revealed in the Season Finale of Season 4 of My Little Pony: Friendship is Magic.
Yes, she became a princess in the season 3 finale.
Yes. In the season finale, the box under the Tree of Harmony opened and the ponies transformed into their Rainbow Power equivalents. They looked exactly like the toyline this design spawned from.
This information has never been revealed, so I can only guess. I would suggested watching the Season 4 Finale when it is released to find out. In my opinion, the Rainbow Kingdom and the Tree of Harmony box are related.
The Season Finale For The Second Season is August 30, 2011.
The mid-season finale (summer finale) is August 30. The whole season 2 finale is sometime in spring 2012.
This information has not been revealed yet. In the Season 4 Finale, this information will be available.
It is very likely that it will be opened in the last episode, though we cannot know for certain. It is possible, for example, that it could be opened in the first part of a two-part finale.
Summer finale is August 30
The Equestria Games arc of My Little Pony seems somewhat similar to the Grand Galloping Gala arc of season 1. So it is logical to conclude that it will be right before or part of the season finale.