And still that only applies to handling "a financial crisis" by giving aid to member state(s) and needs qualified majority (85% in this case so 24 out of 28 votes in both the Council and Commission). Basically how the Council has been setup is that you usually need a unanimous or 20 out of 28 votes to get anything done.
Those votes are only necessary for things like new member additions (which are indeed mostly what the council is for). I think this requires a mere majority, which presumably is equivalent to having a majority in the commission in practice.
But even if it were true, and the only power they have is to fund or defund member states' governments ... that's not a real limitation to their power.
And lastly, if all the power is in the hands of the executive, as it is in Europe, that does not constitute a modern democratic state.
The elections for EU Parliament are not taken seriously in most countries and have had extremely low turnout, by now it is full of right wing idiots from various countries.
You conveniently left out the various side channels that don't even formally exist as European institutions, such as the Troika that decided on the fate of Greece, or the regular meetings of the finance ministers of the Euro Zone, which have had tremendous influence on the fiscal politics of smaller member states. Not to mention the various measures to deal with the Euro crisis by the ECB with the approval of a few large member nations, that cleverly bypassed and sidestepped many treaties and the additional European financial institutions that were created.
For example the current Finnish representative is Jyrki Katainen who is the previous prime minister and his party (Kokoomus) is still a member in the ruling coalition. Even though he probably isn't the most liked person anymore (his prime minister era didn't go that well) he is still well liked within his own party and they probably traded some minister seat for getting him into the Commission. Shit is politics like always but I wouldn't go as far as say that the EU is undemocratic.
Also the ability to speak English isn't that important in EU level. All the big EU institutions are in Luxembourg or Brussels which pretty much makes French and German the main languages. Still there is plenty of translators available when needed.
If Germany wants to keep sending Günther Oettinger as their Commissioner then the only people you can blame are Merkel and her party. Again democracy. If it matters to you make it a point in your elections. I know most people don't as in my experience most people don't have a clue how the EU works. Many of my friends think the Commissioners are just appointed by some elite instead of being each country sending their own just like the head of state is in the Council. Still you can't call a system undemocratic just because people choose not to engage in the process.
Since the previous election, the Council does not pick the candidate itself. Rather it automatically proposes the Presidential candidate of the party that won the European Parliament elections. And each party selects their candidate before the election, and they also campaign and have debates.
All the people in the controlling bodies (well at least the places that should be voted for. Voting for judges etc. is madness) in EU are appointed by the member nations (either by vote or appointed)
European Council: Heads of state of the member nations (president chosen by vote within)
European Commission: One member appointed by each country (so usually someone from the ruling coalition within each country). Sworn to represent the benefits of EU as a whole and not single countries. President proposed by the Council and voted on by the Parliament
European Parliament: Members chosen by vote from each country. President (speaker) voted within.
So both executive and legislative levels are voted in or representatives of a democratically chosen government. Looks like democracy to me.