blue hexagon with a smaller movie-film symbol in the corner
This means they are queueing up for Duty Finder

a reddish icon that might possibly represent a chair
AFK / Away from Keyboard

a pair of red daggers conjoined in a V shape
This player is doing a Guildleve.


Usually any special icons by an enemy name means that they are part of a quest, typically the enemy is strong until you use an item on it to weaken it, and anyone that is on the quest can help kill it.

If you are curious about any icons, you can do a player search for that player and look at their search info. It will show the icon alongside what it means in their profile.