Tail chute:
Probably a very bad idea. Aside from the complexity of certifying such a thing (presumably a different design/size would be needed for each aircraft type), the risk of inadvertent deployment causing it's own disaster would seem much more likely than the incredibly rare situation where it might be of positive benefit.
As far as I can tell from what we know to date, the crew were not aware they were in a stall (you'd have assumed someone would have used the words "we're in a stall" and that the BEA would have reported such in the note) and as such it seems unlikely they would have "punched the button" to deploy such a thing.