Elite Arcanist — ruling 1

You don't choose the value of {X} in the activation cost of Elite Arcanist's ability. It's defined by the mana value of the exiled instant card.

Elite Arcanist — ruling 2

The copy is created in and cast from exile. You must still follow any timing restrictions, such as "Cast [this spell] only during combat."

Elite Arcanist — ruling 3

You can't pay any alternative costs such as overload costs. You can pay additional costs such as kicker costs. If the spell has any mandatory additional costs, you must pay those.

Elite Arcanist — ruling 4

If the copied card has {X} in its mana cost, you must choose 0 as its value when casting the copy. Don't confuse that {X} with the {X} in the activation cost of Elite Arcanist's ability.

Elite Arcanist — ruling 5

If the exiled card is a split card, then X is determined by the combined mana cost of both halves. However, when you cast the copy, you choose only one half to cast. You may cast a different half each time you create and cast a copy.

Elite Arcanist — ruling 6

If Elite Arcanist leaves the battlefield, you will no longer be able to copy the exiled card. If it returns to the battlefield, you'll be able to exile another instant card from your hand, but Elite Arcanist will be a different permanent with no connection to the first exiled card.

Elite Arcanist : règles, fonctionnement et interactions (MTG)

Elite Arcanist is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

When this creature enters, you may exile an instant card from your hand. , : Copy the exiled card. You may cast the copy without paying its mana cost. X is the mana value of the exiled card.

How it works : Elite Arcanist

Original English text — Wizards of the Coast / Scryfall

#1July 1, 2013· Wizards of the Coast
You don't choose the value of in the activation cost of Elite Arcanist's ability. It's defined by the mana value of the exiled instant card.
No other card is named in this ruling.
#2July 1, 2013· Wizards of the Coast
The copy is created in and cast from exile. You must still follow any timing restrictions, such as "Cast [this spell] only during combat."
No other card is named in this ruling.
#3July 1, 2013· Wizards of the Coast
You can't pay any alternative costs such as overload costs. You can pay additional costs such as kicker costs. If the spell has any mandatory additional costs, you must pay those.
No other card is named in this ruling.
#4July 1, 2013· Wizards of the Coast
If the copied card has in its mana cost, you must choose 0 as its value when casting the copy. Don't confuse that with the in the activation cost of Elite Arcanist's ability.
No other card is named in this ruling.
#5July 1, 2013· Wizards of the Coast
If the exiled card is a split card, then X is determined by the combined mana cost of both halves. However, when you cast the copy, you choose only one half to cast. You may cast a different half each time you create and cast a copy.
No other card is named in this ruling.
#6July 1, 2013· Wizards of the Coast
If Elite Arcanist leaves the battlefield, you will no longer be able to copy the exiled card. If it returns to the battlefield, you'll be able to exile another instant card from your hand, but Elite Arcanist will be a different permanent with no connection to the first exiled card.
No other card is named in this ruling.