in my opinion it is wrong only the first part"Then we will see each other. " becouse it might have a secondary sence, teoretikally your translation was good but i was unshure....
I have written an observation there in the end. Both of the meanings are right, depends on how the sentence is pronounced and in what situation is used. If you say to somebody in the end of a discussion, then it means "see you then", if you set a meeting or a date with somebody for, let's say, next day to a specific hour then you can use "we'll see each other then".
"ne vedem" is translated word by word "we'll see each other" and "atunci" is "then". I don't understand what is the problem, the sentences are actually simple and basic... Besides, the translation is requested to be "meaning only" and this what I have done.
"then we will see each other" is quite different from "we will see each other then" - in the first phrase, "then" means "so", or "in that case", whereas in the second phrase it means "at that time". Which is it here?
Actually ... both. Both alternatives are correct. "atunci" can mean "in that case" but also "then". Again, according to the context and how is pronounced.