Isochron Scepter — ruling 1

If Isochron Scepter leaves the battlefield while the activated ability is on the stack, the ability can still make a copy. On the other hand, if the imprinted card leaves the exile zone while the activated ability is on the stack, the copy can't be made.

Isochron Scepter — ruling 2

You cast the copy while the ability is resolving and still on the stack. You can't wait to cast it later in the turn.

Isochron Scepter — ruling 3

If you don't want to cast the copy, you can choose not to; the copy ceases to exist the next time state-based actions are checked.

Isochron Scepter — ruling 4

If you cast a spell "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, those must be paid to cast the spell.

Isochron Scepter — ruling 5

If a spell has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

Isochron Scepter : règles, fonctionnement et interactions (MTG)

Isochron Scepter 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

Imprint — When this artifact enters, you may exile an instant card with mana value 2 or less from your hand. , : You may copy the exiled card. If you do, you may cast the copy without paying its mana cost.

How it works : Isochron Scepter

Original English text — Wizards of the Coast / Scryfall

#1August 7, 2020· Wizards of the Coast
If Isochron Scepter leaves the battlefield while the activated ability is on the stack, the ability can still make a copy. On the other hand, if the imprinted card leaves the exile zone while the activated ability is on the stack, the copy can't be made.
No other card is named in this ruling.
#2August 7, 2020· Wizards of the Coast
You cast the copy while the ability is resolving and still on the stack. You can't wait to cast it later in the turn.
No other card is named in this ruling.
#3August 7, 2020· Wizards of the Coast
If you don't want to cast the copy, you can choose not to; the copy ceases to exist the next time state-based actions are checked.
No other card is named in this ruling.
#4August 7, 2020· Wizards of the Coast
If you cast a spell "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, those must be paid to cast the spell.
No other card is named in this ruling.
#5August 7, 2020· Wizards of the Coast
If a spell has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
No other card is named in this ruling.