Medomai's Prophecy Repeated
Partial answer...


Yes. There is no meaningful difference between an ability triggering twice because of Clockspinning, and a triggered ability being copied because of Strionic Resonator. Either way, the triggered ability has resolved 2 separate times. Note that the choice of card name is only made when the ability resolves, so it will not have been made yet while the ability is on the stack and being copied.
No, the chosen value is not a copyable attribute of Medomai's Prophecy:



  706.2. When copying an object, the copy acquires the copiable values of the original object’s characteristics and, for an object on the stack, choices made when casting or activating it (mode, targets, the value of X, whether it was kicked, how it will affect multiple targets, and so on). The “copiable values” are the values derived from the text printed on the object (that text being name, mana cost, color indicator, card type, subtype, supertype, rules text, power, toughness, and/or loyalty), as modified by other copy effects, by its face-down status, and by “as . . . enters the battlefield” and “as . . . is turned face up” abilities that set power and toughness (and may also set additional characteristics). Other effects (including type-changing and text-changing effects), status, and counters are not copied.


For 1 and 2, the relevant rules are in 607, Linked Abilities. The 2 abilities are linked:


  607.2d If an object has an ability printed on it that causes a player to “choose a [value]” and an ability printed on it that refers to “the chosen [value],” “the last chosen [value],” or similar, those abilities are linked. The second ability refers only to a choice made as a result of the first ability.


However, while rule 607.3 deals with what happens when an ability refers to "the exiled card", and multiple cards have been exiled; there does not seem to be a similar rule to deal with "the chosen value" when multiple values have been chosen.