What is the evidence that sleep invalidates ablution? And how is the Prophet’s — may Allah’s peace and blessings be upon him — not performing ablution after his sleep for the Fajr prayer explained in the Hadith about Qiyam al-Layl with Ibn Abbas?

First: Sleep invalidates ablution (wudu') if it is deep. The proof for this is the hadith of Safwan ibn Assal: "but rather from defecation, urination, and sleep."

Second: The hadith of Ibn Abbas regarding the Prophet Muhammad's (peace be upon him) sleep and his standing for prayer without ablution is specific to him. This is because his eyes would sleep but his heart would not, so he would be aware of any nullifier (hadath) if it occurred. This does not apply to other people.