Praise be to Allah.
The first hadeeth was narrated by Imam ash-Shaafa‘i in his Musnad (365)(and via him by al-Bayhaqi in al-Ma‘rifah (2140). Ash-Shaafa‘i said: One whom I do not have reason to suspect told me from ‘Amr ibn Abi ‘Amr, from al-Muttalib ibn Hantab, that the Prophet, (blessings and peace of Allah be upon him) said: “There is no hour of the night or day but the sky is raining; Allah directs it as He wills.”
This is a da‘eef isnaad. Al-Muttalib is the son of ‘Abdullah ibn al-Muttalib ibn Hantab, a Taabi‘i; he is sadooq but mudallis (says ambiguous things and gives the wrong impression) and narrated a lot of mursal reports, as it says in at-Taqreeb (p. 534).
The shaykh of ash-Shaafa‘i is not named, so he is unknown.
The hadeeth was also narrated by Shaykh al-Albaani in Silsilat al-Ahaadeeth ad-Da‘eefah (4494) via this isnaad. He said:
This is a da‘eef isnaad. In addition to its being mursal, it also includes the shaykh of ash-Shaafa‘i, who is not named. It is not unlikely to have been Ibraaheem ibn Abi Yahya al-Aslami al-Madani, about whose authenticity scholars other than Imam ash-Shaafa‘i had doubts. End quote.
The idea that the unknown narrator is Ibn Abi Yahya is supported by the words of ar-Rabee‘ ibn Sulaymaan: When ash-Shaafa‘i says, “One whom I do not have reason to suspect told me,” he is referring to Ibraaheem ibn Abi Yahya.
Mizaan al-I‘tidaal, 1/58. See also Ta‘jeel al-Manfa‘ah, 2/627; al-Kaamil by Ibn ‘Adiyy, 1/220. Based on that, the isnaad is waahin (weak), because Ibn Abi Yahya was accused of fabricating hadeeth. An-Nasaa’i said: The liars who were known for fabricating hadeeths are four: Ibraaheem ibn Abi Yahya in Madinah, al-Waaqidi in Baghdad, Muqaatil in Khorasan and Muhammad ibn Sa‘eed in Syria.
End quote from Tahdheeb at-Tahdheeb, 9/163
The second hadeeth was narrated by al-Bayhaqi in his Sunan (6717); al-Haakim in al-Mustadrak (3520); at-Tabari in his Tafseer (19/280); and Ibn Abi Haatim in his Tafseer (15247) via al-Hasan ibn Muslim, from Sa‘eed ibn Jubayr, from Ibn ‘Abbaas (may Allah be pleased with him) who said: There is no year that has less rain than another, but Allah, may He be exalted, directs it as He wills. Then he recited this verse (interpretation of the meaning):
“And indeed We have distributed it (rain or water) amongst them in order that they may remember the Grace of Allah, but most men refuse (or deny the Truth or Faith) and accept nothing but disbelief or ingratitude”
Al-Haakim said: It is saheeh according to the conditions of al-Bukhaari and Muslim, and adh-Dhahabi agreed with him.
It was also narrated by at-Tabari (17/84) and al-Bayhaqi (6716) via two isnaads from ‘Abdullah ibn Mas‘ood (may Allah be pleased with him) who said: “There is no year that has more rain than another, but Allah diverts it as He wills.”
It was narrated by al-Bayhaqi (6725) from Ibn Mas‘ood in a marfoo‘ report, then he said: This is how it was narrated in a marfoo‘ report with this isnaad; the saheeh version is mawqoof.
Ibn Katheer (may Allah have mercy on him) attributed it in his Tafseer (6/116) to Ibn Mas‘ood and Ibn ‘Abbaas (may Allah be pleased with them).
It was narrated by at-Tabari (17/84) from al-Hakam ibn ‘Utaybah as his own words.
The report was narrated by Shaykh al-Albaani in as-Saheehah (2461) from Ibn ‘Abbaas, as his own words, and classed as saheeh according to the conditions of al-Bukhaari and Muslim. He also narrated it from Ibn Mas‘ood, then he said: From the above it seems that this report, although it is mawqoof, may be regarded as marfoo‘ because it could not have been said by way of personal opinion or ijtihaad, and because it was also narrated in marfoo‘ reports. End quote.
To sum up:
The report is saheeh in the isnaad from Ibn Mas‘ood and Ibn ‘Abbaas, as their own words; as a marfoo‘ report (i.e., attributed to the Prophet (blessings and peace of Allah be upon him)) it is not saheeh. Can it be regarded as marfoo‘? That is subject to scholarly opinion. What appears to be the case -- and Allah knows best -- is that it cannot be attributed to the Prophet (blessings and peace of Allah be upon him) because it cannot be proven to be from him. But it can be attributed to those from whom it was proven, and it should be limited to that.
And Allah knows best.