1. Factions. When the rules for hated enemy got removed, so did the rules about choosing factions. The God-specific lists state which faction everything is (e.g khorne). The black legion however...doesnt mention anything.
So for Black Legion;
Are they all Undivided?
Do you pick a faction for the army?
Do you pick a faction for each unit and can therefore have some Khornate raptors, and nurgle termies etc.
It is option 3 now, you specify the faction for a formation and summon those daemons or go undivided and pay double for faction daemons but get your own choice.
2. Greater Daemons and factions. The rules state "one greater daemon for each given faction". For the God-Specific lists this is pretty easy; e.g everything is khornate, can only summon blood thirster, so you can therefore have at most one blood thirster on the table.
For Black Legion;
Jon wrote:
If you had a tzeentch unit, nurgle unit, slaanesh unit and khornate unit, could you therefore have 4 GD on the table? (One for each)
If you pay the points for 4 greater daemons you can have 4 on the table at the same time.
Jon wrote:
If you had an undivided unit, and a khornate unit, could you have 2 Blood thirsters? (Undivided can summon any, khornate can summon a blood thirster).
No, Only one greater daemon from a faction at one time.
Jon wrote:
If this is the case, could you possibly get 5 GD onto the table at once? (khorne unit, slaanesh unit, tzeentch, nurgle and undivided)
Sorry only a maximum of 4 GD at one time.
Jon wrote:
If instead it's a limit of one blood thirster, one keeper of secrets etc, then can a single undivided unit summon both as long as it keeps rolling high enough each turn and you had enough pts in the pool?
You can summon different greater daemons in different turns, but you can not mix and match your daemons between different factions in the same formation.
Hope that helps and please forgive the formatting.