Why allies in the game are unique (i.e. only one can be in play at a time)? I know that Gandalf is. What about Faramir? Longbeard Orc Slayer? Brook Ironfist? Gleowine?

The way to tell is by an icon directly to the left of the allies name. If it's present than only one can be in play at a time for everyone playing.

Unique allies (and for that matter attachments, creatures and locations) will have the diamond in a circle symbol before their name. There are several, including the ones you mention except Longbeard - more like Haldir and Landroval in the adventure packs also.