How do I combine the intention of reciting Surat Al-Baqarah for the sake of Allah with the intention of achieving something I desire? And is it permissible to divide the recitation of Surat Al-Baqarah over the day while watching TV or a phone between parts?

It is recommended to recite Surat Al-Baqarah to draw closer to Allah and seek His pleasure. Along with this, one may intend to obtain the promised reward and expel devils, and this does not contradict sincerity. It is permissible to recite the surah (definition) in parts with religiously authorized interruptions, but it is better to recite it consecutively. It is disliked to interrupt the recitation for a phone call, laughter, idleness, or looking at something distracting, unless the speech is an interpretation of the Qur'an and has a valid reason.