The EU is not a nation. It doesn't have a police. Crimes do not take place on its territory, because it has none. So then it'll fall onto the Belgium (or French) police.
Wrt to the rest: just asking questions, right?
It does, Europol. For this case, considering there were raids in multiple different countries within Europe, they probably were involved.
https://www.france24.com/en/europe/20221210-belgium-makes-eu...
2) This is the opposite of convenient. EU would prefer a good working relationship with China given the issues with the US.
3) It was started because there are allegations of corruption.
4) Because no crimes have been committed.
5) Why not ? BlackRock is a global investment bank. It's going to have employees.