Jace's first ability creates a delayed triggered ability that triggers whenever a creature an opponent controls attacks. It doesn't matter which player or planeswalker that creature is attacking.

You pick one of your opponents when Jace's second ability resolves. The ability doesn't target that opponent. All players may see the revealed cards and offer opinions. You (not your opponent) choose which pile is put into your hand and which pile is put on the bottom of your library.

Piles can be empty. If one of the piles is empty, you choose to put all the revealed cards in your hand or on the bottom of your library.

When resolving Jace's third ability, you search each player's library (including yours) and exile the nonland cards before casting any of them.

For each library, the search is complete only when you explicitly say it is. For example, you can look through one player's library, set that library down, look at another player's library, choose a nonland card in the first library, then choose a nonland card in the second library. Don't reveal any cards from those libraries to any other player until you exile them.

You cast the cards by putting them on the stack one at a time, choosing modes, targets, and so on. The last card you cast will be the first one to resolve.

When casting a card this way, ignore timing restrictions based on the card's type. Other timing restrictions, such as “Cast [this card] only during combat,” must be followed.

If you can't cast a card, perhaps because there are no legal targets available, or if you choose not to cast one, it will remain exiled. Jace's ability won't allow you to cast it later.

If you cast a card “without paying its mana cost,” you can't pay alternative costs such as overload costs. You can pay additional costs such as kicker costs. If the card has mandatory additional costs, you must pay those.

If a card has in its mana cost, you must choose 0 as its value.

Planeswalkers are permanents. You can cast one at the time you could cast a sorcery. When your planeswalker spell resolves, it enters the battlefield under your control.

Planeswalkers are not creatures. Spells and abilities that affect creatures won’t affect them.

Planeswalkers have loyalty. A planeswalker enters the battlefield with a number of loyalty counters on it equal to the number printed in its lower right corner. Activating one of its abilities may cause it to gain or lose loyalty counters. Damage dealt to a planeswalker causes that many loyalty counters to be removed from it. If it has no loyalty counters on it, it’s put into its owner’s graveyard as a state-based action.

Planeswalkers each have a number of activated abilities called “loyalty abilities.” You can activate a loyalty ability of a planeswalker you control only at the time you could cast a sorcery and only if you haven’t activated one of that planeswalker’s loyalty abilities yet that turn.

The cost to activate a planeswalker’s loyalty ability is represented by a symbol with a number inside. Up-arrows contain positive numbers, such as “+1”; this means “Put one loyalty counter on this planeswalker.” Down-arrows contain negative numbers, such as “-7”; this means “Remove seven loyalty counters from this planeswalker.” A symbol with a “0” means “Put zero loyalty counters on this planeswalker.”

You can’t activate a planeswalker’s ability with a negative loyalty cost unless the planeswalker has at least that many loyalty counters on it.

Planeswalkers can’t attack (unless an effect turns the planeswalker into a creature). However, they can be attacked. Each of your attacking creatures can attack your opponent or a planeswalker that player controls. You say which as you declare attackers.

If your planeswalkers are being attacked, you can block the attackers as normal.

If a creature that’s attacking a planeswalker isn’t blocked, it’ll deal its combat damage to that planeswalker. Damage dealt to a planeswalker causes that many loyalty counters to be removed from it.

If a source you control would deal noncombat damage to an opponent, you may have that source deal that damage to a planeswalker that opponent controls instead. For example, although you can’t target a planeswalker with Shock, you can target your opponent with Shock, and then as Shock resolves, choose to have Shock deal its 2 damage to one of your opponent’s planeswalkers. (You can’t split up that damage between different players and/or planeswalkers.) If you have Shock deal its damage to a planeswalker, two loyalty counters are removed from it.

If a player controls two or more planeswalkers that share a planeswalker type, that player chooses one of them and the rest are put into their owners’ graveyards as a state-based action.