Casting the card causes it to leave exile. You can't cast it multiple times.

If you leave the game, the card remains exiled face down indefinitely. No player may look at it.

You pay the costs for the exiled card if you cast it. You may pay alternative costs such as emerge rather than the card's mana cost.

An effect that instructs you to "cast" a card doesn't allow you to play lands.

You may look at and cast that card (and spend mana as though it were mana of any type to do so) even if Gonti leaves the battlefield. If another player gains control of Gonti, that player can't look at or cast the card, and you still can.

Gonti doesn't change when you can cast the exiled card. For example, if you exile a creature card without flash, you can cast it only during your main phase when the stack is empty.

The six types of mana are white, blue, black, red, green, and colorless. Snow mana is not a type of mana. Gonti, Lord of Luxury won't let you pay a snow cost using mana produced by a nonsnow source.