Mormon tells us something of the history of these three Nephites and the power of their faith. This is a history out of chronological order in his text. None of these events happened until much later than the time period Mormon is currently describing. This tells us that at this point in his text, Mormon has inserted this section to tell us about the three Nephites, and not simply to accurately record events. Since the three are more important than the chronology, he can break with strict historical timing and give us a picture of the fate of those three in the four hundred years from the current text-time to Mormon’s time.
It is also highly unlikely that Mormon was alive to see all of these events, though we may expect that they began to occur when the Nephites begin to fall into apostasy some two hundred years in the future. It is possible that some of these events did take place in Mormon’s lifetime, as that was a time of great persecution of the believers.
In all of the events Mormon gives for these three, they overcome humanly impossible situations. That they were able to overcome becomes the de facto demonstration of their faith.
Reference: Alma and Amulek are similarly cast into prison and miraculously delivered by the walls falling down. See Alma 14:27.
Mormon himself makes reference to many of these events in his own eponymous book:
Mormon 8:24
24 And he knoweth their prayers, that they were in behalf of their brethren. And he knoweth their faith, for in his name could they remove mountains; and in his name could they cause the earth to shake; and by the power of his word did they cause prisons to tumble to the earth; yea, even the fiery furnace could not harm them, neither wild beasts nor poisonous serpents, because of the power of his word.