If the token isn't exiled at the beginning of the next end step (perhaps because the delayed triggered ability is countered), it remains on the battlefield indefinitely. It continues to have haste.
Flameshadow Conjuring
If the copied creature is copying something else when the ability resolves, then the token enters the battlefield as a copy of whatever that creature is copying.
Any enters-the-battlefield abilities of the copied creature will trigger when the token enters the battlefield. Any “as [this permanent] enters the battlefield” or “[this permanent] enters the battlefield with” abilities of the copied creature will also work.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Seb McKinnon
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
