Is it permissible to pray two Rak'ahs before starting to memorize the Qur'an, and is it necessary to learn it from a Shaykh?

Praying two rak'ahs before starting to memorize, with the intention that they are a desirable but not legislated Sunnah, is not permissible. This is because it is not allowed to innovate an act of worship for which there is no evidence in the Shari'ah. Allah Almighty said: "This day I have perfected for you your religion," and the Prophet, peace and blessings be upon him, said: "Whoever innovates into this matter of ours that which is not from it, it is rejected." There is no evidence for the legislated nature of praying two rak'ahs before memorizing the Qur'an. Believing in their Sunnah status for that purpose falls under bid'ah idafiyyah (innovated addition). However, if one does not believe in their Sunnah status, then there is no objection to it, as prayer is permissible at all times except during the prohibited times.