I don't know but I upvoted your question because obviously it was downvoted because it was not understood you were actually asking a real question :(
Because Duolingo expects you to translate literally, and you switched the order of the sentence.
"to" is not a verb, it's some kind of connector. We can compare it to "=" so the expression on the left side is equal to the expression on the right side. Both expressions are in nominative form.
So, does "to" always combine expressions of like forms, like how coordinating conjunctions in English always combine sentence parts of like form? If so, would this mean that "jest" should be used when the expressions are of unlike form (similar to subordinating conjunctions)?
To is a demonstraitive pronoun. The full sentence would probably be "Jego ofiara to jest jego żona" but the verb is not necessary because it is implied by using the object in nominative case.
I was trying to learn a language... not get wrapped up in a domestic violence case
It could be something a TV reporter or a policeman would say about a crime eg. murder
Is he talking about someone else's wife? If he was talking about his own wife, would "swojego" be substituted, or is that optional?
No, both "ofiara" and "żona" is "jego" (his) - probably the same person's but it could be a wife of some other man.
Potrzebny nam Rutkowski :) The most square-headed private investigator in the world!
English speakers would usually put the sentence the other way round i.e. His wife is his victim
Can anyone explain the rule for when you use "jest" versus "to" in equating.
Because I'm sure "jego ofiara jest nim ofiarą" also works?
Wait... "His victim is him victim"? :> I'm afraid you messed something up a bit.
I will assume that you meant "Jego ofiara jest jego żoną". Or "Jego ofiarą jest jego żona". Both would work, actually.
Well, in general both work in almost any sentence. The difference is that using "to" is kinda like saying "X = Y", so in many sentences the more... descriptive "jest" will sound a lot better.
We would discourage using "X to Y" if X is a person. (Though some sentences like that are probably in the course anyway). I can't say that "Mój brat to żołnierz" is wrong, but it really doesn't sound great. And we would reject that construction if X was a personal pronoun. "On to żołnierz" really sounds too clumsy.
Maybe you've seen it, but I will link anyway: https://www.duolingo.com/comment/16373167
In the complementary sentence where we have to construct the Polish sentence from English, the correct answer shows ofiara as ofiarą.