0-1 restrictions

[Nabterayl]

I agree with JMichael. Death Company specifies one unit per army, and I agree that two primary detachments are part of a single army. Consider page 110: "your Warlord can be from either of the primary detachments in your army." If the two primary detachments are both "in" a singular "army," they cannot each also be their own army.*

Another angle to look at this is:

Does HQ units that unlock some units as troops, carry that "unlocked status" over to the 2nd FoC?

Meaning:

Dante - 12x Squad of Sanquinary Guard
Draigo - 12x Squads of Paladins (not even the biggest Apocalypse games are enough for this )
Crowe - 12x Squads of Purifiers

etc etc..

Depends on the wording, but in those three cases, yes. Each of those special characters says, "In an army that includes ..." and, since the two primary detachments are each part of the same army, it's enough that the special character is present in only one of the two detachments. I can imagine a situation where a special character said, "In a detachment that includes [e.g.,] Commander Dante ..." but I'm not aware of any such cases yet.

Also, do the psychic powers (buffs) and other auras (sanquinary priest FNP) carry to the second FoC?

Well, depends. Strictly speaking, the FoC includes all detachments in your army, including allied and fortification detachments. A Blood Chalice from one Blood Angels detachment would certainly affect Blood Angels from another detachment, because the rule specifies that it applies to friendly units chosen from Codex: Blood Angels. However, a Blood Angels librarian with Forewarning could not cast it on allied Grey Knights, because Grey Knights and Blood Angels do not consider each other friendly units even when part of the same army. The relevant question will usually be whether units consider each other allies or are from the same codex, though, not whether they're from the same detachment.

* Unless we think that, for rules purposes, an army can be made up of multiple armies. I disagree with that notion, though, on the basis that the rules ever only speak of a player's army, singular - even when talking about multiple detachments. Any "army of armies" concept would, as far as I can see, be made up whole cloth.