Nu-Hatta says that you are, of course its really up to you to decide (ie, the choice you're given when you confront Dagoth Ur and he asks you "Are you really Nerevar Reborn?"). The others weren't necessarily predestined to fail, they just happened to have. You might think of them like previous characters of yours that died during the Main Quest...
Right. If the fail, then they haven't completed the prophecy, thus cannot enter the role of Nerevarine and mantle Nerevar and thus are false.
No, failing to mantle Nerevar doesn't make them any less of an
incarnate - that's what the 'failed'/'false' refers to. They were incarnates entering the role of the Nerevarine that didn't succeed, whereas 'false' would imply that they simply weren't an incarnate (and actually sorta implies that they fulfilled the role along with not being an incarnate, which they didn't).