Yes to each questions – all the data is public.

From the principles right here with emphasis mine.

For the Gate:

Reveal the highest Divinity card from every Mythology deck.

For the Divine Theatre surprise:

Reveal all of the playing cards from a Mythology deck of your alternative.

Reveal would imply the playing cards are face-up on the desk for each gamers to see. They usually are not hidden in any method. The phrase reveal is used elsewhere within the guidelines, at all times to seek advice from public data. The setup guidelines make a transparent distinction between face-down Mythology tokens that are then revealed. When you’re taking a Mythology token, the principles say you “draw” two Divinity playing cards; which is distinct from revealing them. You secretly select a Divinity card, it is positioned face-down, after which revealed in Age II Setup.

For query 2 with the Divine Theater, whereas the principles aren’t totally express about it, it appears cheap that for the reason that playing cards are revealed, the order you stack them in can be public data. Technically this level is moot, as a result of the Divine Theater reveals all of the playing cards, then stacks the unused playing cards, however would not flip them face-down once more. Thus each gamers can see the order after anyway. If this was carried out earlier than activating the corresponding Mythology token, that may put the chosen and remaining playing cards face-down on the Pantheon and Mythology decks, so till Age II begins the opposite participant will not know which of the 2 was positioned.

With Enki particularly, the principles say:

When Enki is revealed, randomly draw 2 Progress tokens from these discarded originally of the sport. These tokens are positioned face-up on Enki’s card.

This signifies that whilst you’re making the selection, you and the opponent each know which Progress tokens can be found. The FAQ within the guidelines additionally says:

Q: What occurs if Enki isn’t chosen when the Gate or the Divine Theater are activated?
A: The revealed Progress tokens are returned to the field with these discarded originally of the sport.

This may imply in idea that Enki is revealed twice throughout a sport – first with the Divine Theater throughout Age I, not chosen, after which by being added to the Pantheon usually (or with each the Divine Theater and the Gate in both order). The Progress tokens are nonetheless returned when the Theater/Gate participant would not select Enki, and new ones will likely be drawn the second time.