Serazu said:
Correct. The constant "cannot be saved" effect of Bitter Crone is a character ability. Brienne ignore's the ability of opponent's characters. So she ignores the "cannot be saved" restriction - unless the person who controls her also controls Bitter Crone.
Serazu said:
a. I declare him as attacker and, upon winning a MIL challenge, decide to use his Response. I have to pay 2 gold to my opponent. Right?
Not quite. In order to declare him as an attacker in the first place, you have to pay the 1 gold. Up front, when you declare attackers. It is effectively a restriction on being able to declare him as an attacker. Similarly, when you decide to use his Response, you have to pay 1 gold as part of triggering that Response. So yes, you have to pay your opponent 2 gold, but you pay the gold, one at a time, when you go to do the things Motley charges you for.
Serazu said:
c. If Jhogo had a passive ability on his text box, I still wouldn't pay any gold to my opponent for its activation, since Motley demands payment whenever I decide to trigger an ability, not when an ability is triggered no matter what. Right?
These parts of the question are just asking for confirmation on what a "triggered ability" is. (Even if Deadly WAS considered an ability, it is passive, not triggered.) You don't choose to activate them. They happen whether you want them to or not. So they are not triggered, which moeans Motley does not charge you for them.
Serazu said:
(3.37) Unique Cards Entering Play from the Dead Pile
When putting a unique card into play from your dead pile, that copy of the card does not prevent itself from entering play. Multiple copies of a unique card will prevent one another from entering play from your dead pile, unless those copies would all enter play simultaneously.
b. Cards such as Maegi's Promise are not affected by the above ruling, since they don't return cards into play but into their owners' hand, right?
c. Concerning Retreat, it's not affected either since not only returns a card in hand, but prevents a card from going into the dead pile in the first place, right?
Considering that the FAQ entry starts out "when putting a card into play from your dead pile," do you really need confirmation on these two questions? 
Serazu said:
You are looking at this backwards. There is no general "save" effect. There are only card effects that save. It is not that "saves prevent leaving play by any means unless they are specifically limited." It is that "a given save effect only works against what it says it does." There is no "saving by rule." There is only saving by card effect. So do what the card says.
But yes, anything that "cannot be saved" has no interaction with any effect that uses the word save.