If the oponent declares a Military Conflict in a province with a face up character is legal play Rise the Alarm to put this character into play or is necesary to turn the card face up to play the character?

'Then' effects are contingent on the preceeding event. If there is no face-down card to turn up then you can't put it into play, which means the effect would have no potential to change the game state, which means you could not trigger the ability at all (i.e. play the card).

Are we sure that you can't turn a face-up card face-up? It might just be an action that has no effect. A plain interpretation probably indicates you can't, but I find it difficult to tell when this game wants you to use plain text rather than a strictly-by-the-rules reading so far.

the cost isnt to flip a card up, so long as there is a card to put into play to change the game state i would think it wouldnt matter if the card is face up or down. All costs would still be paid and the effects would change game state so long as something enters play.

The rules are surprisingly clear on how "Then" works: (pg 16 Rules Ref)

The word “Then”
If the effect text of a card ability includes the word “then,” the
text preceding the word then must be successfully resolved
in full (i.e. the game state must change to reflect the intent
of the pre-then aspect of the effect in its entirety) before the
remainder of the effect described after the word “then” can be
resolved.
◊ If the pre-then aspect of an effect does successfully resolve
in full, the resolution of the post-then aspect of the effect
must also attempt to resolve.
◊ If the pre-then aspect of an effect does not successfully
resolve in full, the post-then aspect does not attempt to
resolve

In this case, the text preceding it is "Turn a dynasty card in the attacked province face up." If a card is already face up, it can't be turned face up, so no change of state, therefore the second part can't execute.

Someone can email customer support if they think this is wrong.

I think it's clear.

1. You can't resolve a 'post-then' effect of put into play unless you complete the 'pre-then' effect of turning a card face up.

2. You can't initiate the event if there is no potential to change the game state (by having no face-down card in the province).

Wouldn't this type of play just be a "Charge"? It seemed to me that this card was designed to be a "Charge" for face-down dynasty cards.

I can even see a thematic difference between the two. A face-up dynasty card can see the fight and is just itching to participate, so they are "Charged" in. With a face-down dynasty card, the character is not aware of the fight, and needs to be woken up Paul Revere style, hence "Raise the Alarm".

1 minute ago, ZenClix said:

Wouldn't this type of play just be a "Charge"? It seemed to me that this card was designed to be a "Charge" for face-down dynasty cards.

Yes, assuming it is a face down character card in your province being attacked while military. Doesn't work on face-up cards (to start). And then as long as they are not - military.