As the subject line asks:

1. Do Support cards from my deck which are played onto an opposing Unit still grant me a Loyalty Symbol for building costs purposes?

I ask just to check as the Rulebook seems to suggest that this is, in fact, the case - that they DO grant me a Loyalty symbol due to the rules of ownership, which state on Pg. 17 that, "Players 'own' cards they included in the deck they are playing. Players 'control' cards that they own, unless another player steals control of the card through a game effect."

Absolutely yes!

The control doesn't change even if you play them in the oppo's side. YOU are the controller and the owner (unless some card effects state otherwise).

So, the DO give you loyalty.

Does this also apply if the Dark Elves "steal" one of your units?

In that case, based on the exact wording in the Rulebook, I'd say they do NOT.

I assume that if a Unit of yours changes side, the Attachment does NOT.

That's because a "Unit changing control effect" cannot grant you the control of attached cards.

Now, I don't know if:

- it's like in other games, where, if control changes, attached cards get discarded;

or

- you're still the controller of the card.

DB_Cooper said:

There is no reason to think that attached cards would be discarded. If anything, in CoC, attached cards stay when control changes.

The unit changes control and side. The attachment follow it in the opposing side, as it is attached to the unit (the same thing would happen if the unit was changing zone). The attachment stays under your control as only the unit was targeted by the effect.

How about the situation:

Opponent attacks me with chaos knights, nurglings and maruders, i use take captive, so i take control of knights and want to use my brutal offering - does knights loyality symbol works for me ?

(I play on de capital and have no chaos card in game before take captive)

Yes you now control the Knights so their Loyalty symbol is now yours, not your opponent's.