If All-Fates Stalker leaves the battlefield before its first ability resolves, the target creature won’t be exiled.

Auras attached to the exiled creature will be put into their owners’ graveyards. Any Equipment will become unattached and remain on the battlefield. Any counters on the exiled creature will cease to exist. When the card returns to the battlefield, it will be a new object with no connection to the card that was exiled.

If a token is exiled this way, it will cease to exist and won’t return to the battlefield.

If you choose to pay a spell’s warp cost rather than its mana cost, you’re still casting the spell. It goes on the stack and can be responded to and countered. You can cast a spell for its warp cost only if you could cast that spell. Most of the time, this means during your main phase while the stack is empty.

If you pay the warp cost to cast a spell, that permanent will be exiled only if it’s still on the battlefield when that triggered ability resolves. If it goes to another zone before then, it will stay where it is. If it goes to exile some other way, its owner won’t be able to cast it on a future turn.