Shadow Varys, Daario's and Sir Jorah's Mormont (Where Loyalty Lies) abilities to discard allies, traitor, mercenary, knight from play target themselves if there are not another character with that trait when they come in play?

More specific when you should choose a character can you choose "no character"?

Thank you

They will discard themselves as the effect is passive, it was a response then you would have the option to rigger or not trigger the response, as its passive its going to happen if you want it to or not.

When an effect says "choose and discard 1 ally character," you must choose an ally character if there is one to be chosen. (And with all the cards you name, there is always a legal target to be chosen because, as you noticed, they will always have themselves to choose if there are no other possibilities.)

"No character" is not a valid choice for passive effects - unless the effect specifically says it is with wording like "you may choose 1 ally character and discard it."

Two more question.

(1) Can I choose to discard a knight when Daario comes into play but there is no knight character in play?

(2) Can I choose to discard a knight when Daario comes into play but there is only a Can not be discard knight in play?

While my explanation and reasoning are probably wrong im pretty sure you cant do option 1.

I believe It is not a 'choice' in the same way that theon (pots version), shield dromon islands, or sorrowful man are where the wording allows you to chose an option that you cant fullfill (silly as that sounds) because there will ALWAYS be a viable option available when daario has been played.

Option 2 is certainly not viable as 'cannot' will not allow you to pick that character for an effect that it cannot be effected by. In the same way you cannot choose a 'cannot be killed' character to die for military claim.

Hope that helps

Varys, Daario and Jorah (Street of Silk, too) are valid targets for their own abilities, unless some constant effect gave them an applicable immunity. So if there is no other valid targets. you have to choose them.

Like Uncle_Joker said, "cannot" (like immunity) means the card cannot be chosen as a target, so you have to choose some other target (including Varys, Daario or Jorah himself).