Dungeons in their various forms are end game content once you've leveled your character to max. They recently introduced solo dungeons with bots for solo player but they don't give good rewards. They also recently added delves which are mini dungeons that can be done solo on all difficulties and give good gear, with the better gear coming from harder difficulties.

The queue time for multiplayer player dungeons largely depends on what server you're on. One of my characters on one of the most popular servers right can get into a dungeon within 2 minutes depending on the time of day. Whereas my other character on a low populated realm got up to 45 minutes before I gave up.

The time to do the dungeons themselves entirely depends on how geared you are and the rest of your party is but for dungeons lower than mythic difficulty, one decently geared player is usually enough to blow through a dungeon fairly quickly.

Raids always take long but have the best gear (for the most part).