In some rare cases, you can have a token or a copy of a spell in your graveyard at the moment that an object's delirium ability counts the card types among cards in your graveyard, before that token or copy ceases to exist. Because tokens and copies of spells are not cards, even if they are copies of cards, their types will never be counted.

The number of card types matters, not the number of cards. For example, Wicker Witch (an artifact creature) along with Catalog (an instant) and Chaplain's Blessing (a sorcery) will enable delirium.

The card types in Magic are artifact, battle, creature, enchantment, instant, kindred, land, planeswalker, and sorcery. Supertypes (such as legendary and basic) and subtypes (such as Human and Equipment) are not counted.

If you have three noncreature card types among cards in your graveyard at the time damage is dealt by Deathcap Cultivator, and lethal damage is dealt to another creature you control at the same time, the damage from Deathcap Cultivator won't be from a source with deathtouch.

Because you consider only the characteristics of a double-faced card's front face while it's not on the battlefield, the types of its back face won't be counted for delirium.