Q1: A Formation is a Detachment by itself. Some can also be taken as part of another Detachment, but that's usually about stacking various bonuses together (ex: Deathwatch's various Kill Teams making up a Black Spear Strike Force).
Q2: A Formation belongs to a specific faction (usually the only one that COULD make it because of model requirements) but it's not actually relevant. If you have the models, you can form the Formation with them, and it's just like a CAD or an Allied Detachment. The only place the faction comes into play is how your other/main Detachment(s) treats the newcomers, which will probably be as Battle Brothers in this case.
Ask not the Eldar a question, for they will give you three answers; all of which are true and horrifying to know.