Is the guardian or his deputy given precedence in the funeral prayer, even if there is a regular imam, or is the regular imam more entitled? And is the person most learned in the Book of Allah given precedence over the guardian and his deputy in this case?

The person most entitled to lead the prayer for the deceased is the one whom the deceased requested to pray over him, then the leader of the Muslims (Imam al-Muslimeen), then the deceased's male relatives (ʻasabah) according to their order of precedence. If someone better than the entitled 'asabah relative is present at the prayer, then it is preferable to put this better person forward, but it is not obligatory.