I would take finis
here in the sense "end" = "death". dederint
here is in the subjunctive because Latin uses the subjunctive in indirect questions, and since it's the perfect subjunctive it represents a past tense. Changing it around a bit, I'd finish your translation as "Do not seek -- it is wrong to know -- what end the gods have given me, and what end they've given you,..." -- it could also be "which end" but I don't see too much difference in this case.
MiguelM wrote:I am sure we would be able to help you more if you'd post the sentence.
I can give the first sentence:
Tu ne quaesieris -- scire nefas -- quem mihi, quem tibi finem di dederint, Leuconoe, nec Babylonios temptaris numeros.