>>211841307The Age of Men refers to the fact that magic in the LOTR universe becomes rarer and rarer as times go on. Elves are immortals and bound to the world, but without magic, they fade away into shades. That's why all of them are moving to the West beyond the sea where the magical land there can sustain them. So yes, elves were aware that their time in Middle-earth would be limited and that Men would eventually supplant them. This is less a prophecy and more like an application of the rule of the universe, like if you lived for millions of years you'd take continental drift into account when picking your home.
Sauron has nothing to do with the coming of the Age of Men. He offered the Rings of Powers to the Elves to safeguard their powers and allow them to stay in middle-earth forever, which counts as sorta delaying it, but this was a trick and they didn't fall for it. Orcs, although being elvish in origins in some versions of Tolkien's lore, are never mentioned to have the same problem as elves do, and most likely live only just as long as regular humans.
If Sauron had won, it wouldn't have been the Age of Men (although Men would likely still be amongst his lieutenants) nor the Age of Orcs (because Orcs in LOTR are basically subdued to the will of Sauron or whatever Dark Lord is around), it would've been the Age of Sauron where all but him slave away in hellish labors.