I would say "saliva" myself. While "drool" is the result of "drooling" in the same way that "spit" is the result of "spitting", "drool" as a noun, rather than a verb, is not very commonly used. (As a verb it is commonly used.) Babies don't really spit, because it is a learned action that they are too young for. And changing the second "drool" to "saliva" is more elegant writing in that you use a different word. This is a bit of an unpleasant subject, but I hope that helps.

Do you mean that your friend held her son against her clothes or that your friend picked her son up? Something like that?

Drool is a perfect word there 😊

Drool works well both times in that sentence