Woods wrote:But so, Latin in all its forms was the only language in the Italic sub-branch of the Indo-European languages
Far from it. There were several other Italic languages, but Latin is the only one with descendants in the modern day.
Woods wrote:and it hasn't influenced the Germanic/Slavic/Celtic/Hellenic or Iranian sub-branch in any extremely important kind of way?
I guess it depends on your definition of "extremely important". Latin certainly provided significant vocabulary to various members of the Germanic, Slavic and Celtic families. The Romance languages make up a big chunk of the SAE
sprachbund, so there's some mutual influence there, on levels like grammar and phonology. At the same time, none of that would justify treating Latin as a parent language to anything other than the Romance languages.
N'hésite pas à corriger mes erreurs.