Each BF dungeon has 3 lvls. The third one is very small.
No you don't have to do something special to open, simply find another "fountain" to exit deeper. They are hidden in wall shadows sometimes.
As BF dungeons/quests are generated in a random way => yes, some end lvls are empty and others have 1 to more items/boss monsters.
Post number 187253 shows pic links to display how the end lvls look like, click here
