So if an effect says to deal one facedown/faceup damage card, would this card bypass shields?

Correct, for example: proton bomb

As he said.

Getting dealt a card is not the same as suffering damage. Cards aren't negated by shields and land on the ship. Right now the Proton Bomb deals nearby ships a face-up card. When he comes out Jek Porkins will risk collecting cards if he chooses to dump stress with his ability; R2D2 will not help save him from that ability although R5D8 might.

One of the keys is to watch for the phrase "suffering damage" or "suffer damage." If you see some use of the word Suffer, you know that it follows the normal damage rules of checking for shields, etc.