The two actions provided are not cross-restrictive. Each can be performed once during the same turn by the same minion.

The fact it is Unique has no bearing on the burn option. You cannot use the burn option if you meet the requirement, even if you already have a copy of the card in play.

The action provided by this card is considered to be an action requiring the listed clan/sect/capacity/title (e.g. the action provided by Open War is considered an action that requires an Anarch, the action provided by The Gate of Acheron is considered an action that requires Hecata).