Both the Scroll Scholar and the Seeker archetypes presented in the Pathfinder Field guide are able to be taken as one of two different classes. So my question is: what about both?
Archetypes replace class features, and multiple archetypes can be taken if there is no overlap, but there is nothing substantial written on taking the same archetype with different classes. Can a multiclassed character be a Scroll Scholar(Cleric)/Scroll Scholar(Wizard)? Would the class level stack for purposes of the 1/2 lvl to a knowledge roll (via Diligent student)? What about the 5th lvl additional Knowledge skill of Diligent student? I assume that Secrets Revealed would still only kick at 5th lvl (cleric) or 5th lvl (Wizard), since it replaces features that a 5th character lvl (Such as a 3 cleric/2 wizard) would not have.
1. I don't see any reason why you couldn't be a SS(C)/SS(W).
2. No (well, sort of). In general, abilities from different classes do not stack unless they say they stack. For example, a cleric 10/paladin 10 with channel energy from both classes tracks those classes separately; they do not stack into one 20th-level ability. So you get two separate versions of Diligent Student--one based on your cleric level, and one based on your wizard level.
That said, while the abilities themselves do not stack, if you choose the same Knowledge skill for both classes, the bonuses do stack because they are untyped. So a SS(C) 3/SS(W)3 could allocate both +1 bonuses to Knowledge(planes). (Note that if both class levels are odd and greater than 1, you lose some utility this way due to rounding down.) You could also choose separate Knowledge skills and get more breadth.
3. You get an additional Knowledge skill at cleric 5, cleric 10, wizard 5, and wizard 10. See 2.
4. No, per 2. You get two separate versions of Secrets Revealed (at cleric 5 and wizard 5) with separate caster levels. This can actually benefit you if you simply want more uses of comprehend languages and identify.