Let's says three party members have initiative before me. I want to cast Faerie Fire to give possible advantage. Can my three allies ready their attack saying, “When our bard casts his spell, I attack?”, and that way get advantage in the process?
Yes, that's an option, and it's an effective way to coordination the party's actions.
The DM would have to make a ruling about what order to resolve all their attacks in, but that's not an issue that would prevent them from all taking the Ready action with the same trigger.
Yes they could,but depending on their builds, this may not be an optimal strategy. Readying takes your Action, leaving you only your Reaction with which to act. You could be giving up extra attacks or maneuvers in exchange for a single attack at advantage.
Also remember that Readying an action is always a risk. You are setting up an action that is dependent on a trigger. If that trigger fails to happen, the action (attack, spell or move) "fizzles". If the bard is prevented from casting his spell, the party has lost all of its action for that Turn. That could be devastating.