Hi Luiz, here are my corrections:
1. Many a child has been warned about strangers.
2. No corrections, this one is correct.
3. Many a day will come when we shall be judged.
I've heard "many a/an" much more than "many is the" (which seems like it should be "many are the" since many is plural) and I have never, ever heard "many another" and doubt it is actually in usage at all, if it ever was. So I will speak about "many a/an"; it is an older idiom so to use it now sounds a bit formal or stylized, like the beginning of a proverb. Hope that helps.