Say I have an empty battlefield and use Cloudform to manifest the top card of my library. The manifested card is Heliod, God of the Sun. Can I turn this card face up for the mana cost if I do not have enough devotion to white for it to be a creature?
The rule of thumb I've been told is "it's a creature everywhere but on the battlefield" which would seem to indicate you can't, but I know this is a simplification of the relevant rules. If this can be done, what makes it possible?
Yes, you can turn it face up.
701.31a To manifest a card, turn it face down. It becomes a 2/2 face-down creature card with no text, no name, no subtypes, and no mana cost. Put that card onto the battlefield face down. That permanent is a manifested permanent as long as it remains face down. The effect defining its characteristics works while the card is face down and ends when it’s turned face up.
701.31b 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 115.2b). To do this, show all players that the card representing that permanent is a creature card and what that card’s mana cost is, pay that cost, then turn the permanent face up. The effect defining its characteristics while it was face down ends, and it regains its normal characteristics. (If the card representing that permanent isn’t a creature card or it doesn’t have a mana cost, it can’t be turned face up this way.)
The type of the card on the battlefield is no secret. It's almost surely going to be a creature. ("It becomes a 2/2 face-down creature card [...]"). That means "to show all players that the card represents a creature card" clearly refers to the physical card (rather than the game object), so "represents a creature card" means "would be a creature card if outside of the game".
As such, you only look at its type line, and any characteristic-defining abilities that alter its type (since those function everywhere, including outside of the game).
There's absolutely no chance that Heliod's second ability has any effect because it's an ability that only functions on the battlefield, and the object on the battlefield has no abilities ("It becomes a 2/2 face-down creature card with no text, [...]")
Note that you'll lose Clouldform if you turn Heliod face-up without the devotion needed to make it a creature. Clouldform can only legally enchant a creature.
704.5n If an Aura is attached to an illegal object or player, or is not attached to an object or player, that Aura is put into its owner’s graveyard.
Yes, you can pay the card's mana cost to turn it face up, because it is a creature card. The rules for Manifest, specifically 701.31b say
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 115.2b). To do this, show all players that the card representing that permanent is a creature card and what its mana cost is, pay that cost, then turn the permanent face up. The effect defining its characteristics while it was face down ends, and it regains its normal characteristics. If the card representing that permanent isn't a creature card or doesn't have a mana cost, it can't be turned face up this way.
As long as Heliod is face down, just like when it is in another zone, it doesn't have the ability that says it is not a creature, so the card is still a creature card.
The reminder text for Manifest (from Cloudform) also hints at this
To manifest a card, put it onto the battlefield face down as a 2/2 creature. Turn it face up any time for its mana cost if it's a creature card.
