Each Bomat Courier you control has its own cache of cards. Bomat Courier's last ability only puts those cards into your hand, not those of any other Bomat Courier.

If Bomat Courier leaves the battlefield before you activate its last ability, any cards exiled by its triggered ability remain exiled face down for the rest of the game. If you somehow return the same Bomat Courier card to the battlefield, it will be a different object with no connection to those face-down cards.

You can pay the cost of “discard your hand” even if your hand contains zero cards.