They don't have to know, they could just get lucky. With a hero as squishy as Sniper though, you can easily tell after one swing whether or not it's the real one because the illusions will take like 1/3 of their HP in the first hit.
And I'm not disputing manta as a late game item, but I don't see how it's better than SnY or just straight BKB for the mid game. You can always disassemble and sell the Sange once SnY is no longer ideal.
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Lich is definitely good for that. I'd probably add Crystal Maiden, too, since Frostbite makes it easy for you to get a little gold and XP from creeps and her aura means she doesn't really have any need for MP regen, just straight INT. Both heroes are really good for learning zoning on, too.