Battle forged armies using formations

I have a question that I believe I have right.

If I'm taking a detachment of dark eldar as per FOC, I also want to bring a detachment from coven supplement.
If I want to use a couple of the formations detailed in coven supplement, do I have to, as well as the two formations, take the obligatory 2 hq and elite choices?
Or as the two formations fulfill these requirements (two Haemonc and two grots) do I not have to?
Or is it that simply the formations form their own detachments and disregard the FOC altogether?

The rulebook seems to state that formations can be taken irrespective of FOC and still retain battle forged status?

Thanks

Correct - formations are a type of detachment with their own requirements and units that are the only options you may access

As such, they have no FOC

Ok, so the allied detachment can be home to two formations? Or would it be two allied detachments?
As a final question, and this may actually be a different topic altogether.

Can you take a formation as a primary detachment? In battle forged? And how would that work in regards to the rules?
Would it be that one formation would be your entire primary detachment?

I'm having an argument with a friend, and he is adamant that a formation doesn't fulfil battle forged criteria?

Cheers

Formations are detachments.
An army consisting of detachments is battle forged.
A Formation can be primary detachment. Warlord can only come from primary detachment. So the Haemi from the Dark Artisan Formation can be your primary detachment und thus, Warlord.

An allied detachment cant be home of 2 formation, as a formation is its own detachment.
An allied detachment has a specific set up as described in the BRB.
Two Formations are two seperate detachments.

I see, thank you.