Francisco, Fowl Marauder

To have two commanders, both must have the partner ability as the game begins. Losing the ability during the game doesn't cause either to cease to be your commander.

Once an ability that causes a creature to explore begins to resolve, no player may take any other actions until it's done. Notably, opponents can't try to remove the exploring creature after you reveal a nonland card but before it receives a counter.

Once the game begins, your two commanders are tracked separately. If you cast one, you won't have to pay an additional {2} the first time you cast the other. A player loses the game after having been dealt 21 damage from any one of them, not from both of them combined.

In some unusual cases, noncreature permanents may explore. For example, if the creature card returned by Defossilize is somehow not a creature once it's on the battlefield, it can still explore. You'll take all the same actions, and you may end up putting a +1/+1 counter on the permanent. (Note that some effects target a creature, and those effects would still require a legal target to have it explore.)

If no card is revealed, most likely because that player's library is empty, the exploring creature receives a +1/+1 counter.

Some spells or abilities might cause a creature to explore multiple times in a row. If you reveal a nonland card when a creature explores and leave it on top of your library, then the creature explores again immediately afterwards, you'll reveal the same card again.