This question has sparked some discussion in my country between lvl 2s, i also tried the live rules chat, but i haven't gotten a satisfying answer.

B controls a Grafdiggers Cage (in part: Creature cards can't enter the battlefield from graveyards or libraries.) and player A casts Soul Summons (Manifest the top card of your library.), manifest says “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.” so Grafdiggers Cage prevents the card from being put onto the battlefield (so far so good).

Now, player A activates his Domri Rade (Look at the top card of your library. If it's a creature card, you may reveal it and put it into your hand.)

1: can A put the card into his/her hand if it is for example an instant, since manifest turned it into a creature?
2: does the card stay face-down after drawn and is thus, for all intents and purposes ‘lost’?
3: how does a face-down card on a library generally work?

My guess would be 1: no, since only the backside of the card is a creature (but how does that work? the rules for ‘revealing’ a card do not say that the front face of the card is revealed)
2: no, a library is a face-down pile of cards so drawing it effectively turns it face-up
But i have no sources in the comprehensive rules that prove or disprove these things.

If manifesting a card fails to put that card onto the battlefield somehow, nothing happens. The card remains where it is and does not continue to be affected in any way by the past attempt to manifest it. Everything works exactly the same as if no attempt had been made to manifest it in the first place.