But this is open to question, because when the Prophet ﷺ went out to pray for rain, he did not instruct his Companions to fast.
As for what the author first mentioned—repenting from sins and redressing wrongs done to others—these are appropriate measures. Fasting, however, is an act of worship that requires evidence to establish it. Since this occurred in the time of the Prophet ﷺ and he did not instruct his Companions to fast, there is no basis for commanding it.
However, we may say that if he chose Monday—not making it a regular established sunnah—so that it happened to coincide with the fasting of some people, there would be no harm in that.
But to make it a regular established sunnah that the prayer for rain should only be held on a Monday, or to command the people to fast, is open to question.
His statement, “And charity,” means that he also instructs them to give charity. Charity may be considered appropriate here, because it is kindness toward others, and kindness is a cause for mercy, as Allah Most High says:
“Indeed, the mercy of Allah is near to those who do good.” [al-A'raf: 56]
Rain is itself mercy, as Allah Most High says:
“It is He who sends down the rain after they have despaired and spreads out His mercy.” [al-Shura: 28]
The charity intended here is not obligatory charity, but voluntary charity. As for obligatory charity, withholding it is a cause for rain to be withheld from the sky, as the Prophet ﷺ said in the hadith narrated from him: “Whenever a people withhold the zakah due upon their wealth, rain is withheld from the sky from them.” (1)