Learn Spanish (Latin America): Ojalá el genio pudiera conceder mi deseo.

To form the imperfect subjunctive, you always start with the plural "they" form of the preterite (simple past) tense. For poder, the preterite form is pudieron. Drop the -ron at the end to get the irregular stem pudie-, and then add the ending -ra for the third-person singular, resulting in pudiera.

Why does this sentence use the imperfect subjunctive (pudiera) instead of the present subjunctive (pueda)?

The word ojalá expresses a hope or wish and always requires a subjunctive verb. Using the imperfect subjunctive (pudiera) here means this is a hypothetical or unlikely wish right now, translating to "I wish the genie could...". If you used the present subjunctive (Ojalá el genio pueda...), it would mean you think it is a real possibility: "Hopefully the genie can...".

I thought genio meant "genius". Why is it translated as "genie" here?

Genio is a versatile word. It can mean "genius" (a highly intelligent person) or "temper" (like having a bad mood). However, in fairy tales or contexts involving granting a wish (conceder un deseo), el genio translates to "the genie".

Why isn't conceder conjugated in this sentence?