'Out of curiosity' means I'm not curious at all. Right?
Not quite.
The "out of" in "just out of curiosity" is nothing like the "out of" in "out of gas".
Instead, that "out of" means "stemming from" or "originating from" – it means the speaker is curious, and that curiosity is prompting the person to ask a question:
Just out of curiosity, how long have you two been dating?
If the person really isn't curious, but is asking the question anyway, that would start with something like:
Not that I really care, but, how long have you two been dating?
It's also worth noting that, in the phrase "out of curiosity," we are alluding to the first meaning of curiosity, and not the second (definitions from NOAD):
curiosity
1 a strong desire to know or learn something
2 a strange or unusual object or fact
Lastly, it's worth pointing out that this doesn't sound natural at all:
"We are all here to discuss our curiosities about learning English."
I think you mean to say something like one of these:
We are all here to discuss how we are curious about learning English.
We are all here to discuss our curiosity with the English language.
Best Answer
Grow apart is ordinarily used of two or more entities:
You could say that you grew apart from X and you would probably be understood; but apart from is ordinarily used to designate a 'location' (you did your "growing" at some distance from X) rather than a 'direction' (you became more and more distant from X).
The usual idiom, particularly with ideas, attitudes, behaviors and the like, is grow out of:
This usually implies some deprecation of X—you became more aware or more mature and realized that X was deficient.
A more common alternative to grow out of X is transitive outgrow: