What are the reasons behind Al-Bukhari's omission of certain wordings in some of the hadiths he narrated, and did others mention them, or is there manipulation in printed editions, or were they not in accordance with his conditions?

What is mentioned in the two hadiths is an ambiguity in the wording, not an omission or manipulation of it. This ambiguity comes from some of the narrators, and is not the work of Al-Bukhari. One of the narrators made ambiguous what Ibn Mas'ud did when he erased a surah from the Qur'an out of reverence for it. As for the statement of Aisha (may Allah be pleased with her), "Abu so-and-so," she meant Abu Hurairah. It appears that the narrators who explicitly mentioned his kunya narrated the speech by its meaning, and this is permissible with no blame.