You declare the attack, it will turn into a gambit next turn. That is to give everyone ample warning and preparation time, in case someone decides to oppose you. Mind opposing parties do not necessarily have to be declared openly in a gambit, some of the weaker houses might prefer to work from the shadows...especially emergent houses are built to profit from such plays.. So if Varalin wants to save Kol she could do so with concealed cards...of course once her cards are revealed it basically becomes obvious who is on which side.
As for Deathslayer, as always when cards are assigned to mortals i will offer you a variety of folks which are already existing and might fit the role or might be interesting for it and you can choose among them. Alternatively we work something out as to who might come conveniently into existence for it.
Kol has no hand, he might however get support from other unaligned cards if they exist or are in the field. Currently there are none so theres that.
Deathslayer vs Lifeslayer is always a win for Deathslayer unless somebody plays coin or obelisk, to change the outcome.
He is not irrevocably bound to it, should he become an effective non-entity he will be reduced to uncarded figure of importance. Basically sealed evil in a can style. Lorewise, the Deck would retract its protection of him, since he has become worthless as a card.
Mechanics wise he is no longer Lifeslayer at that point. The Card would go back into the deck so to say until somebody else plays it on someone else...or frees Kol. Should Kol become Lifeslayer again the responsible party would need to start a gambit to free him. In the other case Kol would be decreased to a last house level king. (so he would be the same level of strength as Varalin currently is) Mechanically if somebody were to free him, he would be an utterly unbound npc card doing its own thing, but not truly belonging to a house. At that point he could be more or less be enticed to help out in gambits or even join a house as a Knight or for those gods dwelling alone in their houses, as a consort.
That was a tangent but to answer what you probably intended with that question: nope you cannot seperate the two, it will be done by me when i deem Kol to be basically irrelevant to the story (basically if you seal him away and i notice that lifeslayer won't become a thing ever again if it stays with him) at which point he will be quietly freed of his power, something only the Lifeslayer card holder will be informed of, to avoid you guys camping in front of his prison ready to kill him.