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The cards are exiled, not put onto the players' hands. Players can look at and play the exiled cards, but can't do anything else with them (the exiled cards can't be discarded or cycled, for example).
Replacing your draws isn't optional. You can't draw cards from your own library, even if all your opponents' libraries are empty.
If more than one Shared Fate is on the battlefield, you choose which one replaces each card draw, but you can replace a draw only once.
You need to pay the costs of any cards you play from the Exile zone. This could be a problem if you don't have the right colors of mana available.
Each Shared Fate tracks only the cards it exiled. If the Shared Fate which was responsible for a card being exiled leaves the battlefield, putting another Shared Fate onto the battlefield will not allow you to play that card again.
