MQ doesn't feature new dungeons. This is neat I guess but I never bothered with MQ. Harder puzzles never appealed to me.
Technically, no. But the dungeons were changed around for the Master Quest version. It also feature 1 or 2 new enemies.
It all depends on how you look at it-- the dungeons are all in the same locations, have the same map layouts, and same bosses. But the enemies, puzzles, locked doors, and pretty much everything else that effects the way you play through the stage are significantly different. Therefore, describing them as "new" could hardly be considered inaccurate.
As far as new enemies go, I don't know what you're talking about. There aren't ANY new enemies in MQ... that is unless you mean old enemies in new places... but even then there are A LOT more than 1 or 2.