In trying to answer, I feel like Grandpa Simpson " Well, you're really asking two questions there. The first one takes me back to 1934..."
Okay, let me try and answer as best I can:
To start, just in case you missed it, GW recently changed the rules on subfactions such that you can't mix and match if they replace the same keyword (I think Chaos Daemons get an exception). So you could have Black Heart and Cult of Strife in the same list, as they replace <KABAL> and <CULT>, respectively. However, you couldn't have Black Heart and Poison Tongue in the same army (note: army
, not detachment
) as they both replace <KABAL>. "Do I lose rules when I put a Cult and a Kabal in te same detachment?"
Each detachment has to be declared as Cult, Kabal or Coven. Let's say you have a Patrol and choose Poison Tongue. Every Kabal unit in that detachment will get the Poison Tongue bonus. You can also add Cult or Coven units to the detachment. If you do, your Kabal units will retain the Poison Tongue bonus but the Cult/Coven units won't get any bonuses from their specific Cults/Covens.
There is one exception - a Realspace Raiders (RSR) detachment. This requires an Archon, Succubus and Haemonculus and at least one troop choice from each of the respective subfactions. The Archon also has to be the warlord. If these conditions are all fulfilled, you can declare the detachment a RSR detachment and the Kabal, Cult and Coven units in it will all
get their respective bonuses. "What about when I use two patrols?"
As above, you can choose whether each of the patrols is a Cult, Kabal or Coven. You're free to have multiple Kabal, Cult or Coven patrols or to have a combination of Cult, Kabal and Coven. The only thing you can't do is have two different Kabal/Cult/Coven detachments. So (as above) you could have 2 Poison Tongue Patrols but not a Poison Tongue and a Black Heart.
Also, if every detachment in your army is a DRUKHARI Patrol, you don't lost any CP points for the additional patrols."What happens when I use e.g one detachment World Eaters and one Detachment Khorne daemons?"
I think it will depend on the individual books. If I'm not mistaken, CSM and Chaos Daemons both have 8th edition books right now, so at time of writing you might not lose anything, except CP for the extra detachment(s).
However, 9th edition books have what you could call a Loyalty Ability. This is a special bonus you get for playing a given faction without allies. For example, if Dark Eldar take Eldar allies then all Dark Eldar units will lose Power from Pain.
(There are also exceptions - e.g. Imperial armies can use various assassins and imperial agents without forfeiting their loyalty bonuses. Likewise, DE will apparently be able to take a single Harlequin Patrol without losing PfP.)
I imagine CSMs and Chaos Daemons will get loyalty rules when they get their updated codices, but for now the detachment CP is probably the only downside of allying them.
Phew. I think that covers anything but if you have further questions or if I haven't explained something very well and you'd like me to elaborate, please feel free to ask.