I'm less worried about a capitalist democracy like the USA than the EU in this regard. The EU is an undemocratic construct where moralist positions far outweigh the EU's own interests, so it's much more like the USSR than the USA could ever be.
This will help you to get the facts straight: https://www.youtube.com/watch?v=h4Uu5eyN6VU
Democracy doesn't require a lot of parties, it requires that the people actually have the power to elect someone in charge. The EP is powerless and none of the EC members are elected or can be removed by a public vote.
No, this problem has been studied and democracy (that is, rule by the people) empirically requires an electoral system that had the capacity to support multiple competitive parties; to the extent systems artificially limit the option space they produce results that are not representative of the will of the people.
First democracy: ca. 500 BC
First political parties: ca. 1800 AD
We could discuss in detail whether the EU system or the US system enforces more artificial limits, in the end the EC remains much less democratic due to its relative power and independence from the electorate.
Isn't the European Commission elected by the European Council, and formed of commissioners nominated by the democratically elected leaders of each member state?
Democracy doesn't have to equal direct election.
Prototypal modern, organized political parties started to emerge in the 1700's. Do you think before then that everyone was an independent and had no common goals? Political factions predate even the first demcracy. There where a number of competing, and from many accounts solid, factions in both the greek and roman governing systems, which where for all intents and purposes a party.
More concerning is the inability of the European Parliament to repeal legislation, but things are gradually moving to change this.
And now let's look at the past 3 presidents: always the same routine, the EP gets presented with 1 candidate and can say yes... or yes. Awesome democracy.
Living in a small, entirely democratic EU country, I can't say I'm impressed with how the Commission was formed and it's also obviously an inferior system to that of the USA.
The power to directly elect or remove the top spot is certainly an important facet of democracy, maybe even the most important, but it's still just one of many measures. to be honest I don't think it's really that meaningful to talk about one system being "more democratic" than another, or that "entirely democratic" can apply coherently to anything except some kind of anarchist utopia.
That said, there is such a thing as the global [democracy index](https://en.wikipedia.org/wiki/Democracy_Index) in which the US comes well below the UK and plenty of other EU countries. Note that Norway, also a constitutional and hereditary monarchy, tops the list.
This is rather meaningless as an indicator of the quality of the political system. The USA was downgraded there in 2016 for various reasons (probably mostly "Trump anxiety") while the political system was left unchanged.