Philosopher's Stone

If I have two (e.g. via Replication), do the effects stack?

Yes.

How does the Philosopher's Stone work with multi-element cards, such as King Arthur and Queen Guienevere? Would King Arthur, who requires 4 mana, cost 3 or 0 Mana to cast using the Stone

Cards that have different element symbols count as a spell of each of those affinities. So Arthur and Guinevere are each an Air spell, an Earth spell, a Fire spell, and a Water spell, all at the same time. But you are still casting them together as a single spell. So, assuming Arthur is your spellcaster's first spell of the turn, the Stone will offer a discount of 1 mana for Arthur, making him cost 3 . This also means that when Arthur is played he uses up the Stone for that 's turn because he's simultaneously the first , , , and played this turn. So the cannot continue to use the stone that turn.