Look at the card as it exists in your graveyard to determine whether it can enter the battlefield. For example, Sculpting Steel can be put onto the battlefield as a copy of a creature, but Phyrexian Metamorph can't be put onto the battlefield, even if it would copy a noncreature artifact.

Manifesting a card from a graveyard or library is an impossible action while Grafdigger's Cage is on the battlefield.

If an effect exiles a card from a library and allows a player to cast it, that player may do so. The spell is cast from exile, not a library.

Players can still play lands from graveyards or libraries if an effect allows them to do so.