Shadoko asks some questions
"- if an engine flameout happened, was an ACARS to be transmitted?"
I can't say. But, I'd presume that would be fodder for a message. But past discussions make me think it might not be for some reason.
"- is a spinning "posture" making a stop to the satellite transmission (so, no more ACARS)?"
A spinning condition would not necessarily stop ACARS. They were in a position for a very high angle view of the satellite. The ACARS antenna has a very big "main lobe". So a mere spin should not take the satellite out of the main lobe of the antenna. It would, perhaps, show up in satellite logs as degraded signal to noise ratios (technically speaking Eb/N0 - energy per bit divided by noise energy.)
"- in the event of a vertical stabilizer rupture, is the cabin depressurization mandatory (and followed by an ACARS)?"
I believe you mean "inevitable." In the earlier thread there were pictures of the tail structure. Given the damage visible on the stabilizer it can come off in that manner without compromising the cabin. The entire tail structure probably cannot come off (violently) without compromising the cabin integrity. There is no indication that either departed the rest of the plane before the plane hit the ocean surface.
I hope the middle answer helps. That's more or less my field (my technical life's first love, you might say). The other two answers are "educated guesses" at best.