Does "arrive" in this sentence mean the grandson is arriving for a visit or does it mean the grandson is being born? Or can it mean both?
Can be both. But in case of born, it is more usual to say: "O meu neto nasce em dezembro"
why do you need "O" in front of this kinds of sentences? What is the purpose? Seems rather clear without it.
The definite article is to point a specific identified one. But the possessive "my/meu" already does that, so, in cases like this, article is absolutely unnecessary. But Portuguese accept them, there's no difference.
not really. in many occasions we include the article, especially in Portugal
when talking about days you use "na"/"no". but when talking about months or year you don't use de definite articles ("a"/"o") so it's "em"
ex: meu neto chega na quarta.
meu neto chega no dia 21 de janeiro de 2016. meu neto chega em janeiro de 2016. meu neto chega em 2016.
In italian nipote is used both for grandsons and uncle's nephews is in portuguese two different words?