What is the authenticity of the hadith: "There is no hour of night or day except that the sky rains in it, Allah directs it wherever He wills," and the hadith: "There is no year that rains more than another year"?

The first hadith has a weak and fabricated chain of transmission. Al-Muttalib ibn Hantab is truthful but frequently engaged in tadlis (concealing the name of a shaykh) and irsal (omitting the Companion in the chain). The shaykh of Imam Al-Shafi'i is unknown, and it is possible that he is Ibrahim ibn Abi Yahya, who was accused of fabricating hadith.

As for the second hadith, it was narrated from Ibn Abbas and Ibn Mas'ud, may Allah be pleased with them both, that they said: "There is no year with less rain than another year, but Allah Almighty directs it wherever He wills." This is authentic from them as a mawquf narration (attributed to a Companion), but its attribution to the Prophet, peace and blessings be upon him, is not sound. It has the ruling of a marfu' narration (attributed to the Prophet), yet it should not be attributed to the Prophet, peace and blessings be upon him, unless it is firmly established from him.