My question is, do you choose a single opposing character or an opposing character per character using this TA?

Is this true for similar abilities such as the Gordanians?
And in the case of the Full Moon ability, do you roll once for all or do you roll once for each character using it?
And, in general, other abilities that state "once for all characters" or similar wording?

"Choose one for all characters using..." means choose once and it is applied to all of them. If it is meant to be once for each, it will say "for each" or something similar.

Also related: If a roll is required "once for all" it is not able to be rerolled with Probability Control since the roll is not tied to a specific character. So, in your example, the Full Moon roll can't be rerolled.

OK, so you only choose a single opposing character for both JL:GL and Gordanians, and you roll a single die for the Full Moon. Thank you for clearing that up.