Makes rules that are enforceable across member states (admittedly by proxy mechanisms)
Those “proxy mechanisms” make things very different than a typical government. Also not everything that the parliaments says is required to be enforced in member states. A lot of the proposals are recommendations and even the ones that are actually about regulation have to be transposed into member state laws in some way those countries see fit and there’s a lot or margin there.
No, there isn’t. The founding treaties of the EU don’t allow for the creation of a European army as the EU is about peaceful economic cooperation and and also a bunch of other reasons.