First, if you'll be able to finish the semester despite being homesick, it's definitely a sensible thing to stay for (at least) a few more months.
Yes, I do think that's one of the main questions to be answered. On the other hand, I'll need some time to move and find a place to live in my destination city; I'll probably need to take over the dorm at least a month or up to three before the uni starts. I'm thinking that perhaps finishing up a course or two (half the semester) and then moving could be the best thing to do.
Regarding your living situation, another 3 moths of living together might impact your relationship negatively. I take this from the fact that you've both already considered splittig. Alos, in my opinion/experience, 3 months of time are well worth getting your own place.
I definitely could see it putting some strain on our relationship, which would be a shame since I think we could end it on very good terms.
How do you think might your feelings evolve after you split and you move back to your country? Is there a chance that your are lacking space now but you would want suffer being far away from her?
I'd obviously miss her, but there are a lot of different factors such as goals in life, personality compatibility and lack of common interests that make me think (and I think she agrees) that it's not a productive relationship long term regardless. I think the concept of relationship comfort is a really good description of why we're together, honestly. We function fine living together, but there's not much "relationship" - we struggle to find anything to do together, we don't interact much, intimacy is basically gone at this point. Also, I have felt a lack of space and freedom, thinking that it was a bit sad to be "locked down" from the age of 16 and onwards in a relationship that, in the end, is not really giving either of us the life we want.
Based on the level of detail you provided, I would suggest a conservative approach: Move out, give each other space, don't break up just yet. See what will happen in the following month or two, then decide.
I might have to try that. I'm not sure how easy it is to find a living space, especially for short periods of time, but perhaps.