Is it permissible to seek divorce from a sterile husband, knowing that he is a good man, due to an intense desire to have children and a feeling of incompleteness from not having them? And is it permissible for others to perform Istikhara prayer on my behalf?

Marriage aims for procreation, and the Prophet, peace and blessings be upon him, encouraged marriage for increasing the Muslim population. There is no blame upon you for seeking divorce from your husband due to not having children; this is not considered selfishness or an objection to Allah's decree. The husband has the right to refuse divorce except in exchange for a compensation (fidyah), and patience in this matter is better. Seek guidance yourself through Istikhara (prayer for guidance).