What Surahs from the Qur'an should be recited during Qiyam al-Layl, and is it permissible to open the Mushaf and read from it during prayer if the Surahs are long?

It is not obligatory for the worshipper to recite specific surahs after Al-Fatiha in obligatory or supererogatory prayers. However, it is sunnah to recite long surahs during the night vigil (Qiyam al-Layl). It is permissible to recite multiple short surahs to obtain great reward, for the Prophet, peace and blessings be upon him, said: "Whoever prays at night reciting ten verses will not be recorded among the negligent. Whoever prays at night reciting one hundred verses will be recorded among the devout. And whoever prays at night reciting one thousand verses will be recorded among the Muqantireen (those who receive immense rewards)." There is no harm in reading from the Mushaf during prayer for the Imam or for one praying alone, and if a memorizer Imam is available, that is better.