Is it permissible for me to set a daily portion of dhikr (remembrance of God) for myself, and is it permissible to learn from a Sufi shaykh (learning matters of self-purification and the like)?

The Sunnah suffices the Muslim with the absolute and restricted remembrances mentioned therein, and it is the best guidance. However, there is no harm for one who takes a specific litany for himself from the already legislated remembrances and commits to it for the purpose of managing time and disciplining the self, as long as he does not believe that it is a special Sunnah and possesses a special virtue. As for the second question, most Sufis today follow a methodology full of innovations in purifying the souls; therefore, one must be cautious of them. If you are in need of a guide, then be keen to choose someone known for the soundness of his methodology in belief and action, and who follows the path of the Prophets and the Salaf.