'I would not wish it for me' is not idiomatic english, although apparently accepted. No-one would say that.
The given answer 'I would not wish for it' is not a good translation as it does not convey the reflexive element.
Idiomatic english would be 'I would not wish that for myself' or '... on myself' or 'I would not wish for that myself' which have subtly different meanings depending on context.
Is 'es' here the indirect object? I have noticed that German syntax prefers to place the ind. object before the dir. one, but 'es' kind of looks like a dir. object here: Ich wünsche es. And does mir act like an indirect object, or is it just the reflexive part of sich wünschen?
mir is the reflexive pronoun in the dative form. So when you wish for something in English, it's like you are "wishing it to yourself" when you say it in German. I think this occurs because when you wish something for someone else you also have to use the dative, like in the sentence "Ich wünsche dir/Ihnen einen schönen Tag."
'I would not wish for it for myself' Is this different in meaning to the official answer? Once again, the example lacks context.
No not really different.
"I would not wish for it for myself" "I would not wish it for myself" are probably the best answers for the original German "Ich würde es mir nicht wünschen." We use reflexives in English too.
"I would not wish for it" - the given answer, does not convey the reflexive in English. There is a difference between wishing for something for yourself and wishing, say, something would happen because you think it would be a good thing.
"I would not wish it on myself" is generally used when the "it" is a bad thing or someone else might want it but you would regard it as a bad thing. For example "If I did X then Y might happen and I wouldn't wish that on myself!" Similarly "I wouldn't wish that on him" would be used sympathetically to express a desire that something bad didn't happen.
"I would not wish for it myself" i.e .without either "for" or "on" is not reflexive. It might mean you don't want something to happen to someone else. It is idiomatic way of emphasizing that "I" am not wishing for it as opposed to other people especially, perhaps someone recently referred to.