The cleric spell list. You can learn and prepare other spells, but they are not on your class spell list.
Only with cleric spells.
Generally, if an effect grants you an additional spell known without specifying what list to pull it from, you use your class's normal rules for learning spells. In the case of the archivist, that's cleric spells only, except when copying scrolls. However, a given feature may work differently, so make sure you refer to the specific text of the ability.
It depends on the source of the domain; almost every class that grants a domain has its own rules for how to apply it to non-clerics. In the case of the classes from Complete Divine, archivists are non-clerics who use a spellbook, so they use the rules listed for wizards on page 20.