Generally, if you exile Fae of Wishes with Mind's Dilation, you may cast either the normal part or the card (Fae of Wishes) or its Adventure part (Granted).
In general, if an adventurer card is in exile or in a player's library, its Adventure part is ignored when determining what kind of card it is (C.R. 716.4). Thus, for example, for the purposes of Mind's Dilation, Fae of Wishes is a "nonland card" because that card doesn't have "Land" in its normal type line (C.R. 205.1, 205.2a, 716.4).
In general, however, if an effect allows you to cast an adventurer card, you may cast that card either normally or as an Adventure (C.R. 716.3). (The exception given in C.R. 716.3d applies only if a spell that was cast as an Adventure was exiled as it resolved due to the Adventure replacement effect, not if an Adventure spell or adventurer card was exiled by any other means.) Thus, for example, since Fae of Wishes is a "nonland card" for the purposes of Mind's Dilation, Mind's Dilation lets its controller cast that card either normally (as Fae of Wishes) or as an Adventure (as Granted), especially since Mind's Dilation doesn't restrict what a player can cast that card as (C.R. 109.5).
In general, if an adventurer card is in exile or in a player's library, its Adventure part is ignored when determining what kind of card it is (C.R. 716.4). Thus, for example, for the purposes of Mind's Dilation, Fae of Wishes is a "nonland card" because that card doesn't have "Land" in its normal type line (C.R. 205.1, 205.2a, 716.4).
In general, however, if an effect allows you to cast an adventurer card, you may cast that card either normally or as an Adventure (C.R. 716.3). (The exception given in C.R. 716.3d applies only if a spell that was cast as an Adventure was exiled as it resolved due to the Adventure replacement effect, not if an Adventure spell or adventurer card was exiled by any other means.) Thus, for example, since Fae of Wishes is a "nonland card" for the purposes of Mind's Dilation, Mind's Dilation lets its controller cast that card either normally (as Fae of Wishes) or as an Adventure (as Granted), especially since Mind's Dilation doesn't restrict what a player can cast that card as (C.R. 109.5).
See also this thread and this thread.
EDIT (May 14, 2022): Some rules were renumbered in the meantime.
EDIT (Jun. 6, 2022): Correctness edit.