Is it better to take the Imamate exam in another city to achieve imamate and guidance, even if it leads to missing the night vigil (qiyam al-layl) and supererogatory prayers (nawafil), or to take it in one's hometown to preserve the night vigil and supererogatory prayers?

We advise taking the exam in the other city. The desired benefit of you becoming a guide who teaches people is a transitive benefit whose good is widespread, and it is more deserving of attention than abandoning some supererogatory acts due to an excuse. If you rectify your intention and are sincere in your resolve, it is hoped that Allah will extend His aid to you so that you can study without it greatly affecting your supererogatory acts of worship. And if you miss some supererogatory acts due to travel or extreme fatigue, it is hoped that their reward will be written for you, based on the hadith: "If a servant falls ill or travels, Allah records for him what he used to do when he was healthy and resident."