(A)-(IV): "Indistinguishable from" is the standard collocation. We say something is indistinguishable FROM something else, not "with," "to," or "for."
(B)-(I): "Affinity with" is correct because "affinity" describes a natural connection WITH something or someone.
(C)-(II): "Dissimilar to" is the proper usage. Things are similar TO or dissimilar TO other things in standard English.
(D)-(III): "Mistake X FOR Y" is the correct phrase. When confusing one thing for another, we use "for" to indicate the incorrect substitution.