Do Manifested or Morphed creatures count as tokens?
No.

Both the morph and manifest abilities that allow you to have a face-down permanent apply only to cards (morph works on creature cards in your hand, and manifest on cards from your library). The other two ways to have face-down permanents (Illusionary Mask and Ixidron) apply either to creature cards or nontoken creatures.

If some effect (e.g., Fated Infatuation) makes a token copy of a face-down creature, it will simply be a 2/2 creature with no text, name, type, nor mana cost. It cannot be turned "face up" because being "face down" is NOT a copiable characteristic. Therefore the token is not actually "face down".