You can choose any card name, even if that card doesn’t normally have an activated ability. You’re not limited to the names of cards you saw in the opponent’s hand.

You can’t choose the name of a token unless that token has the same name as a card.

Anointed Peacekeeper’s third ability applies to all opponents, not just the opponent whose hand you looked at.

Activated abilities contain a colon. They’re generally written “[Cost]: [Effect].” Some keyword abilities (such as equip) are activated abilities and will have colons in their reminder text. Triggered abilities (starting with “when,” “whenever,” or “at”) are unaffected by the last ability of Anointed Peacekeeper.

An activated mana ability is one that produces mana as it resolves, not one that costs mana to activate.

Anointed Peacekeeper’s last ability affects cards regardless of what zone they’re in. This includes cards in hands, cards in the graveyards, and exiled cards.