Does reading one hundred verses at night mean any one hundred verses, or do they have to be long or equivalent to Surat al-Baqarah, in order for one to be recorded as having prayed the entire night, as stated in the authentic Hadith?

The hadith was not narrated with the wording mentioned. The closest wording to it is: "Whoever recites a hundred verses in a night, for him will be written the devotion of a night." In another narration: "Whoever recites a hundred verses in a night will not be written among the negligent, or will be written among the devout." And another wording: "Whoever recites a hundred verses in a night will be written among the devout." And another wording: "Whoever recites ten verses in a night will not be written among the negligent, and whoever recites a hundred verses will be written among the devout." The apparent meaning of these hadiths is that reciting a hundred verses is general, from any part of the Qur'an.