Anafenza's last ability cares only what the card would be in the zone it's moving from, not what it would be in the graveyard. For example, if a land card you control becomes a creature due to an effect and then dies, the land card will be exiled. But if a creature card with bestow is an Aura when it would be put into the graveyard, it ends up in the graveyard.

Anafenza's first ability can target any tapped creature you control. That creature doesn't necessarily have to be attacking.

If your opponent discards a creature card while Anafenza is on the battlefield, abilities that function when a card is discarded (such as madness) still work, even though that card never reaches a graveyard. In addition, spells or abilities that check the characteristics of a discarded card (such as Chandra Ablaze's first ability) can find that card in exile.

While Anafenza is on the battlefield, abilities that trigger whenever a nontoken creature your opponent owns dies won't trigger, as that card will never reach that player's graveyard. (Token creatures will still go to the graveyard briefly before ceasing to exist.)