Rulings

The "number of times it's been cast from the command zone" includes the most recent time. For example, the first time you cast your commander from the command zone in a game, if you spent mana from Opal Palace's last ability to do so, it will enter the battlefield with a +1/+1 counter.
If you have two commanders, the last ability adds one mana of any color in their combined color identities.
If Opal Palace's last ability produces two mana (most likely due to Mana Reflection) and you spend them to cast a commander, that commander enters with two counters for each time it's been cast from the command zone this game.
If you don't have a commander, Opal Palace's last ability produces no mana.
If your commander is a card that has no colors in its color identity, Opal Palace's last ability produces no mana. It doesn't produce {C}.