Stable empires have always been those that offered the greatest degrees of sovereignty to those under their rule, and I think that this should be somewhat self evident. When you try to enforce conformity across an empire, you're going to face resistance and even the mightiest of empires cannot sustain itself without a solid internal foundation.
[0]https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELE...
European countries were literally at each other throats until 1945, then we gradually built the European Union.
But when you do things like force countries to accept immigrants they may not want to accept, or demand cultural conformity on issues that are not well received, you're undermining your union. Historically religion is a great example here, as it was always the thing that divided people the most. And the Empires that thrived were those that allowed people to maintain and practice their own religion. In modern times socio-political values largely act in the same role, and also form the same divisions. The only difference is it just comes from personal ideology instead of scripture. Unfortunately we still seem largely stuck at the era of calling each other blasphemers and calling for crusades.
Are you referring to what period?
Good luck showing causality here. Single EU nations have no way of competing with EU or China until we have real single market. In theory we have single market, but in practice every country introduces regulations on top of European ones and extending to other European countries is huge pain in the ass (and costs fortune).