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

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.

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

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.