Is it permissible to complete the recitation of the Qur'an from the point where I previously stopped in the middle of a page, or must I start from the beginning of the page?

If you wish to stop your recitation and leave, you should pause at the end of a Surah (definition) (chapter) or an Ayah (verse), and it is better to do so after the completion of a meaning. There is no consideration for the beginning or end of a page; the rule is the end of the Ayah. If you wish to resume recitation, begin with an independent phrase in meaning from where you stopped or elsewhere, after Al-Isti‘adhah (seeking refuge with Allah) and Al-Basmalah (in the name of Allah) if it is the beginning of a Surah (except for Surat At-Tawbah (definition)), otherwise you have the choice. It is not permissible to begin with a phrase that distorts the meaning or transforms it into a meaning that contradicts Islamic law, such as "Allah’s hand is chained."