Learn Swedish: Varken vattenskadan eller brandskadan var ju ditt fel. - Neither the water damage nor the fire damage was your fault, you know.

This is the negative concord constraint in action. Because varken ... eller (neither ... nor) acts as the subject of the sentence here, it carries the negation all by itself. You only need a separate negative word like inte when the varken ... eller phrase is the object, as in Jag orsakade inte varken vattenskadan eller brandskadan (I caused neither the water damage nor the fire damage).

Does starting with varken trigger the V2 (verb-second) rule, and if so, why is var the fifth word?

The V2 rule is in effect, but the entire phrase Varken vattenskadan eller brandskadan functions as a single subject block. Since that whole subject phrase takes up the first slot in the sentence, the verb var rightfully takes the second slot.

What does ju add to the meaning of this sentence?

ju is a modal particle that implies the listener already knows or agrees with what is being said. Here, it translates nicely to 'you know' or 'after all', softening the statement and acting as a shared reassurance that the listener is not to blame.

Why is it ditt fel instead of din fel?