What is the authenticity of the hadiths that indicate that deceased Muslim children enter Paradise, and is there any proof that they will be nursed by the Houris?

A believing woman should seek her reward from Allah Almighty for the loss she has experienced, for "Wondrous is the affair of the believer! All of his affairs are good, and this is not the case for anyone except the believer. If prosperity befalls him, he is grateful, and that is good for him. And if adversity befalls him, he is patient, and that is good for him." As for the children of monotheists who died before puberty, they are in Paradise under the care of Ibrahim (peace be upon him). They are the "da'amees of Paradise" who will meet their parents and enter Paradise with them. However, there is no confirmed report about them being nursed by the Hur al-Ain.