A: The card Play All But 1 says: Play all but 1 of your cards. If you started with no cards in your hand and only drew 1*, draw an extra card.
So, the player in question, starting with zero cards, must play the card they draw. If that card turns out to be Play All But 1, then, as per the directions on that card, since they “started with no cards in [their] hand and only drew 1” then they need to draw an extra card. Since the current Rule is Play All But 1, they are left with 1 card in their hand, and their turn is over.
*Note that in some printings, this second instance is written out, but, to avoid conflicts with Inflation, it should actually be a numeral as written here.