In what way to you think the EU is not democratic? All member states are required to be stable democracies. The governments of members guide policy and the institutions. It has an elected parliament. Most members joined after holding referendums. The only country that has decided to leave did so in a referendum. It's hard to see how it could be very much more democratic.
Mainly the EU is a bureaucracy, so many of it's heads are appointed just like any bureaucracy, but they answer to democratically elected leaders.
I'll defer to the wealth of online information on this topic.
That said even my pro EU friends don't make the claim that the EU is democratic. Usually pointing out that the U.K. and the US are not that democratic either. The U.K. being a monarch with a hereditary House of Lords and the US being a federation (see previous election).
I also hold the view that democracy does not scale well beyond city states and that a federation is preferable so long as the federation has constitutionally limited powers. This way demicracy still dominates the affairs of the citizenry. Unfortunately federations have a habit of extending their powers which is where the political system becomes less democratic. I would argue that the EU has increased their powers over time and the system has become less democratic. I would argue the same rule applies to the US.
It's a detail. They are effectively an advisory body. They can recommend changes to legislation but the Commons can always overrule them.
If you're talking about the Crown estate, it is outside their control and the revenue has been at the disposal of Parliament since the reign of George III. Estimates of the private wealth of the Queen put her at about number 302 in the UK rich list. Hardly a gatekeeper of national wealth. Do you actually know anything at all about the UK's constitutional arrangements?
Mainly the EU is a bureaucracy, so many of it's heads are appointed just like any bureaucracy, but they answer to democratically elected leaders.