Hey there, Nonnie!
Well, unlike Noldorin (banned!), or Khuzdul (sacred!), there is absolutely NOTHING secret about Sindarin! There’s nothing hindering anyone in the whole of Middle-Earth from learning it.
Considering that Sindarin has been basically the Lingua Franca of Middle-Earth since the First Age, it’s probably a really good idea that Gimli learn it. More Elves in Valinor will speak Sindarin than Westron, I expect!
(begs the question also – did Frodo, Bilbo, Gimli etc. have to learn Quenya to converse in Aman? I honestly don’t know… but imagine older!Gimli doing lots and lots of language lessons, a frown on his white-bearded face 🙂
Oh, we are DEFINITELY going to see Thranduil’s reaction to Gigolas! But I am taking a sliiiiightly different approach to the ‘telling the parents’ situation. 😀