If Nicol Bolas leaves the battlefield after his creature face's activated ability has been activated but before it resolves, the card remains in whichever zone it moves to. It won't be exiled or return transformed.

When Nicol Bolas's enters-the-battlefield triggered ability resolves, first the next opponent in turn order (or, if it's an opponent's turn, that opponent) chooses a card in their hand without revealing it, then each other opponent in turn order does the same. Then all the chosen cards are discarded at the same time.

In some rare cases, a spell or ability may cause Nicol Bolas to transform while it's a creature on the battlefield. If this happens, the resulting planeswalker won't have any loyalty counters on it and will subsequently be put into its owner's graveyard.

Each face of a double-faced card has its own set of characteristics: name, types, subtypes, abilities, and so on. While a double-faced card is on the battlefield, consider only the characteristics of the face that's currently up. The other set of characteristics is ignored.

You can activate one of the planeswalker's loyalty abilities the turn it enters the battlefield.

While a double-faced card isn't on the battlefield, consider only the characteristics of its front face. For example, Nicol Bolas has the characteristics of its creature face in the graveyard, even if it was a planeswalker on the battlefield before it was put into the graveyard.

The mana value of a double-faced card is the mana value of its front face, even while it's on the battlefield with its back face up. For example, the mana value of Nicol Bolas, the Arisen is 4.

A double-faced card enters the battlefield with its front face up by default, unless a spell or ability instructs you to put it onto the battlefield transformed, in which case it enters with its back face up. The back face of a double-faced card can't be played.

Nicol Bolas, the Arisen has a color indicator on its typeline. This color indicator means that it's a blue, black, and red permanent.

In a multiplayer game, if a player leaves the game, all cards that player owns leave as well. If you leave the game, any permanents you control from Nicol Bolas's third loyalty ability that came from other players' graveyards are exiled.

If another permanent that isn't a double-faced card (such as Mirror Image) becomes a copy of Nicol Bolas, the Ravager, activating the ability to exile it and return it transformed will only exile it. It won't return to the battlefield at all.