1) No, although when it's not said it's implied. "I really like eating ice cream. On the other hand, I know it's bad for me." "On the one hand, I really like eating ice cream. I know it's bad for me, though." "On the one hand, I could stay up all night watching movies and eating pizza..." 2) Yes. They have slightly different meanings. The first sentence suggests that the language is lost first, and then the culture is lost (because the language is gone). The second sentence suggests that the two things happen at the same time (or the order could depend on the intonation). 3) It makes sense, but it feels a little rigid. The simple present tense suggests certainty - whereas the previous sentences use the conditional 'would'. I might expect to kind such a sentence in a piece of persuasive writing.

1. I don't think that those have to go together in writing, but it makes sense to have them go together. I'd call it a stylistic choice. 2. Your re-write is correct grammatically, but it doesn't carry the same meaning. Eventually implies that it isn't going to happen right now but rather in the future, at an unknown time. At least that's my take on it 3. Both make sense, I would say 'The culture disappears with the language', unless you want to have a more violent imagery for the reader.