Is it compulsory that the one who memorized the most of the Qurān leads the prayer? And if so, is this always the case, or does this change if he is the guest for example?

It is recommended and not obligatory, so if someone else leads and his recitation of al-Fatihah is sound the prayer is valid. The owner of the house and the one in authority have more right to lead than the guest even if the guest is more learned and a better reciter, unless he gives him permission to go forward.