(1) Was it ever determined, whether on-screen or in Trek literature, if the Enterprise-C was completely destroyed by the Romulans at Narendra 3? Or was the ship either captured or salvaged? I know that Yar bartered herself in return for the survival of the, well, survivors, but not HOW they survived or how many of the one hundred-ish that had made it to 2366 survived the confrontation with the Romulans when they came back to 2344.
This story is not told on screen, in "Redemption" or in other episodes or movies. It's told in the Sherman&Shwartz book Vulcan's Heart
, where the E-C destroys some of the Romulans attacking Narendra III, Romulan infighting claims more of those ships, and afterwards the attacking Romulans discuss (within earshot of their Federation and Romulan prisoners) the reasons for the defeated E-C unexpectedly exploding on them after the actual battle.
We don't learn whether the warp drive of the E-C really "degraded" on its own, whether the E-C crew heroically scuttled their own ship, or whether these particular Romulans are just lying their eyes and pointed ears full in order to conceal the fact that the Starfleet ship was indeed captured.
(2) If the C was indeed captured or salvaged, was it ever determined if the Romulans discovered that the ship had indeed been to their future and returned? I would imagine the ship's chronometers would have been off by however many hours it spent in 2366...
does not delve into this, and one possibility there is that the Romulans never had a chance to study the ship much. Certainly none of the heroes or villains express knowledge of time travel. But it appears likely that Tasha Yar would at some point reveal this to her captor, as there's no real reason she should attempt to keep it a secret, and there would be many obvious "unexplainables" about the affair, prompting the Romulans to investigate and interrogate.
(3) Were the C survivors that Yar traded herself for repatriated to the Federation at some point? Or, like the Khitomer survivors in the TNG episode, were they left to live their lives on a remote planet?
AFAIK, this is not really followed up in the S&S books. Yar is the only prisoner who in Vulcan's Heart
is ascertained to survive beyond the last page, but Castillo appears alive in the SNW short story The Fourth Toast
by Kelly Cairo, a minor continuity hiccup the closer specs of which I don't know.