Except the elected bodies can choose to accept or reject the proposed legislation. The Commission is more equivalent to our Civil Service, who are also unelected.
Not really, there is a EU civil service which is equivalent to our civil service.
There isn't an exact mapping between our parliamentary process and the EU's.
Over here, elected representatives propose and vote on laws, and appointed lords review it. The elected representatives can force laws through the lords because they are only allowed to reject a certain number of times. The civil service does all the work in putting the wordings together and doing the appropriate research, and then actually implementing them.
In the EU, appointed members propose laws, and elected representatives suggest amendments and vote on the final decision. The Civil service serves a similar role to in the UK.
The key point is that the MEPs, cannot propose laws in any shape or form. they are completely beholden to the commission. Their biggest power is the power to refuse a proposal from the commission. Its a semi-democratic governance of an autocracy.
Anyway, these points and debates are now of the past.