Do levels taken in a prestige class of the same kind of magic (arcane/divine) as a base class stack with a character's existing caster level? For example, if a Wizard 4/Rogue 3/Arcane Trickster 2 character levels up and takes another level of Wizard (becoming W5/R3/AT2), do they qualify for the Forge Ring bonus feat (requires caster level 7)?
The rules seem to say both yes and no. Under the definition of caster level:
A spell's power often depends on its caster level, which for most spellcasting characters is equal to her class level in the class she's using to cast the spell.
But Arcane Trickster says:
When a new arcane trickster level is gained, the character gains new spells per day as if she had also gained a level in a spellcasting class she belonged to before adding the prestige class. She does not, however, gain other benefits a character of that class would have gained, except for additional spells per day, spells known (if she is a spontaneous spellcaster), and an increased effective level of spellcasting. If a character had more than one spellcasting class before becoming an arcane trickster, she must decide to which class she adds the new level for purposes of determining spells per day.
Furthermore, if a character has multiple spellcaster base classes of the same type of magic, do all levels from these classes stack, does their highest base class combine with their prestige class levels, or do they just use the highest level base class? e.g. what would be the caster level of a Wizard 5/Sorcerer 3/Loremaster 2 character?