Will God answer my prayer for the guidance of a specific person, knowing that God guides whomever He wills?

Supplicating for the guidance of people is legitimate. The verse "Indeed, you do not guide whom you like" is not to be understood as prohibiting it, because the Prophet, peace and blessings be upon him, prayed for people's guidance after its revelation, such as his supplication for Daws and Abu Hurayrah's mother. The verse negates the guidance of divine bestowal (hidayat al-tawfiq) for people, which is a power possessed only by Allah. However, this does not prevent asking Allah for the guidance of those one loves.