Are the claims that 'Umar ibn al-Khattab beat Abu Hurayrah and accused him of lying, and that 'A'ishah accused Abu Hurayrah of fabricating hadiths, true claims with sources?

The accusation against 'Umar ibn al-Khattab and 'A'ishah (may Allah be pleased with them both) that they accused Abu Hurayrah (may Allah be pleased with him) of intentionally lying about the Messenger of Allah (peace be upon him) is unfounded. Rather, 'Umar used to appoint Abu Hurayrah to positions and accept his narrations. As for 'A'ishah, she did not reject Abu Hurayrah's narrations; rather, she disapproved of his rapid method of transmitting hadith. In doing so, she was not challenging his truthfulness but rather his style of delivery. His appointed time of death came while he was the Amir of Madinah, and he led her funeral prayer.