Nymeria Sand

Challenges Action: Choose an opponent's character. Until the end of the phase, that character loses a challenge icon of your choice, and each Sand Snake character you control gains that challenge icon.

Can I choose a challenge icon, which the opponent's character does not have at the moment?

Since there is a rule about (negative) modifiers (RR page 13), I believe, that the character can have a negative amount of challenge icons, although it is treated as having none.

Same situation arises with

Maester Caleotte

Reaction: After you lose a challenge in which Maester Caleotte is participating, choose a character. That character loses a challenge icon of your choice until the end of the phase.

Short answer; yes. Long answer - yes .

In answering your questions here so far, you seem to have an excellent grasp on the RR in general - and thank you for pasting the relevant text, it always makes it easier to answer.

I'd actually recommend you check the (ffg-owned fansite) cardgamedb rules forum , which is more active and the answers are a little better curated to reference in the long run.