The Commission President as well as the entire Commision has to be approved by majority vote in the European Parliament. Maybe elected isn't the proper word, but there is democratic control. Besides, the nominees are nominated by their respective elected governments. They don't appear out of the blue.
The European Council is not democratic and it never was supposed to be. Maybe it should be abolished, maybe it shouldn't - while not as democratic as electing senators to a European Senate, it gives the member states a stronger, quicker and more direct say into the European Union. I do not claim to hold all the answers.
Yes, we need to give the European Parliament the power of initiative as well. And with the UK leaving us, maybe we actually be able to achieve that.