I agree with almost everything you said, just two things:

I'm not for pushing anyone, I prefer them to follow their natural desires
It does make sense, but I think that for "pushing" it is meant that you are being said: you don't need to worry because most of the jobs (if not every single one) doesn't have gender, so don't be afraid to be ambitious and follow your natural passions.

Society is kinda on the same path, and if we allow time and energy on this matter, then we won't be able to alow it elsewhere. My point here was mainly to say that if we start to take spend time and energy for understanding something without any results because the answer isn't pleasing, then it might not change many things.
Society is not just like a family, it's a leap forward. Society is characterized by synergy, that is to say, that only part of the resources of the society would be used (and they are being used), in the meanwhile all the other parts work on other aspects, it is never on pause. So, again I don't see a problem here.

No issue with that, I only have issue when it's considered as universally true and obectively right. First step is education, but do you think education would entirely fix the problem and would work on everybody?
Yes, that would open another huge topic. I am also not 100% okay with considering something indisputable, especially if it comes from humans minds ahaha
Regarding education: it's a very complicated thing to make in practice, for the fact that we are all different therefore we need different treatments, but I'm sure when i'm saying that the childhood stage it's so important as so delicate and if specialists or adults, in general, gave more attention to it, people would have fewer complexes in their future life.

In this specific case, then fail to assimilate or integrate the newcomers would indeed be something to think about (but if Italy is in the same case as France, then we're more into multiculturalism than "integrationism" or "assimilationnism" nowaday) for various reasons (like economical reason, because integration is expensive).
About that ahahah we are still debating whether we should let them in (for those who come form some African states) or not. I see a very little spirit of multiculturalism where I live.