Why can’t faith be disproved? If someone has faith in a prophet and it is demonstrated that a prophecy is false, then their faith is contrary to reason. Disproved.
As far as the claim that the history of Josephus is a forgery, Josephus was known and appears in other documents external to his own writings, but taking you on your own terms, show me even an arguably credible contemporary history by an American Indian/Lost Tribe from Judah talking about Christ in the Americas. Or lost tribes of Jews in the Americas. The two faiths are not even comparable. The Mormon faith runs contrary to reason and evidence. The Christian faith is consistent with reason.
You're absolutely right. There is no evidence that the Lost Tribes made it to America. Archeology hasn't found proof of the Lamenites, Jaredites, or Nephites. There is no scientific evidence for Mormonism. But of what instance is the lack of scientific evidence? It's not going to change a Mormon's mind - he doesn't believe in Mormonism because of scientific evidence.
The Christian faith is consistent with reason.
It is internally consistent, but rests on fundamental presuppositions. They are ones which I hold too, but you have to recognize your presuppositions and note that they are neither provable nor universally shared.
Those examples you gave are conditional and in some cases they were fulfilled. The civil war happened and there was mayhem. The United States army was defeated by the Mormons — see the Utah War or Buchanan’s blunder etc.
Anyway, by your standards, there are plenty instances of prophecies in the Old Testament and the New Testament not being fulfilled.