Does manifest use the stack?

The effect defining its characteristics works while the card is face down and ends when it's turned face up. 701.34b Any time you have priority, you may turn a manifested permanent you control face up. This is a special action that doesn't use the stack (see rule 116.2b).

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Consequently, what happens when a manifest card dies?

When your manifested card dies, Gift's trigger tries to return that card to the battlefield. If it was an instant or sorcery: It want to return to the battlefield face-up, but that's simply unacceptable to the game rules for an instant or sorcery to be on the battlefield, so it stays in the graveyard, and so does Gift. Can you look at manifested cards? No, your opponent may not look at the card, since 707.5 only allows the controller to look at it. No, a manifested card does not go on the stack; manifesting is an action taken as part of a spell/ability resolving.

Moreover, is mtg manifest casting?

Does manifest count as casting a creature? No. Manifesting a card is always part of another spell or ability resolving. Can you manifest a Planeswalker? If an instant or sorcery is manifested and the card Cloudshift if played on one it will remain in exile. A manifested planeswalker card that is cloudshifted will still enter the battlefield, so it will still have its starting loyalty counters.

Can you Unmorph a manifest?

Yes. If a creature card with Morph is manifested, the permanent it becomes may be flipped for either its creature cost or its morph cost.