Is there a Hadith reported from the Prophet, peace and blessings be upon him, with the meaning: "Wash your penis and testicles and perform ablution" for someone who is in a state of major ritual impurity (janaba) and unable to perform a full ritual bath (ghusl)? And is this Hadith authentic, and what is its text if it exists?

The hadith (definition) is authentic and agreed upon. It was narrated by Al-Bukhari from Abdullah ibn Umar, in which Umar mentioned to the Prophet, peace and blessings be upon him, that he experiences janabah (definition) (major ritual impurity) at night. The Prophet, peace and blessings be upon him, commanded him to perform ablution (wudu') and wash his private parts, and then sleep.

This hadith is specific to the person in a state of janabah who wishes to sleep. He performs ablution and sleeps, and is not required to perform ghusl (definition) (ritual bath) before sleeping. However, if he intends to pray, ghusl is obligatory for him, and washing the private parts and performing ablution is not sufficient, unless water is unavailable or he fears harm from using it, in which case he performs tayammum (definition) (dry ablution) for each prayer.