Identified errors:
This is not correct for Romania: officially it’s Surname + Given-name, live in Hungary.
Not true for Greece, it’s just First-name + Surname. It just happens that some Surnames are derived from the father’s name (think “Anderson”).
Historically, yes; however, they passed a law some years ago to allow for the mother’s surname to be the first surname, as it happens in Portugal. Nonetheless I am not sure how popular this is.