Should it be accepted to say "we eat lunch and drink wine" and not have to add the second we? It is implied already, is it not?
It is implied, but the translation here should include the second "we". However, it will be accepted soon.
May I am mess it up, but, right after "but" and "because" you cannot repeat the pronoun (it is if the subject don't change); however, other cases you have the option.
I assume because to be + ing is a different time form. "We are eating" implies that the process is still ongoing right now while "we eat" can be a general statement