To clarify, dungeons, duty quests, and FATEs have a maximum level. If you are over that level, you will be synced down to the duty's maximum level. This means your stats are what you'd have at that level, your gear caps out at the stat caps per item for that level (varies depending on slot and stat and level), and as you've noticed, you don't get the use of abilities over that level. The idea is that when you're doing lower level content you won't be drastically better than someone of the proper level so folks won't moan and gripe about getting a newbie in their newbie level dungeon.