They are not descendants, but reincarnations. And they are captured because (as reincarnations) they have access to heavenly artes (aka magic and other stuff), thus, they make a good asset in the war against Garam. The guys with the mask can block their heavenly artes, to prevent them from jail breaking.
Their main reason for travelling is because they want to remember more about their past, and discover the location of the "magical plot thing with a weird name", because they fear that Mathias would use it to destroy the world.
Those black things are the Ratio Soldiers that Asura fought, because they recognized Luca as Asura, the soldiers transformed into them by sheer rage.
They were asked to rescue Ange, Hartman told them that she was also a reincarnation and thus was captured by the army. They decided to help her and with the possibility that she may know something about the magical trinket. Ricardo was hired by someone to rescue Ange, and because she paid him to not only break his contract but to also hire him as bodyguard, he travels with them.
Kongway is not a reincarnation. Can't say more about that.
More or less, that's the gist of it. It's been a while since I played Absolute Zero translation (DS Innocence), so I don't remember the terms and translations used.