You've raised some excellent points and one that I was unaware of was the fact that UK cabinet members need not be elected members of parliament. I learn something new every day!
Special advisors can wield significant influence, but it should be remembered that decisions aren't ultimately taken by those advisors. How our elected MPs come to make decisions is their own business, but if we aren't happy about that process they may find themselves not being returned at the next election. Similarly if we are dissatisfied with individual MPs, or an entire government, we can throw them out at the next election.
The Council of the European Union makes laws by qualified majority and the manner in which they do so directly contravenes the UK's constitution.
I'm not sure that I follow your logic on the European Commission. It is the executive branch of government within the EU, yet only commission members get to decide who joins. Member states propose commissioners, but the commission reserves the right to reject those proposed candidates. It was though this system of self-appointment that Ursula Von Der leyen came to be president of the commission. A list of candidates was drawn up by member states in the European Council, yet each and every one of those candidates was rejected. To resolve this unfortunate state of affairs, the commission put forward their own candidate and the European Parliament duly voted again - unusually that vote provided a single option - Ursula Von Der Leyen - and even in a one horse race she almost failed to secure the presidency!
One other huge issue is the European Court of Justice. This court is one of the EU's seven institutions, but isn't counted as one of the three legislative institutions. Despite not being a legislative institution, the ECJ regularly and deliberately ignores EU treaties and rewrites them as they see fit. This single issue was probably the main reason we came to hold a referendum on EU membership. No matter what member states agree, the ECJ has the power to ignore that which it finds inconvenient and implement new laws as and when it pleases.
Would you accept only having a say in local council elections and then trusting those councillors to decide who should govern the whole country? Neither would I but, while not directly comparable, that's as close an analogy as I can think of
I'm glad we agree on the need for EU reform, but it was on this very subject that David Cameron was sent home with his tail between his legs and found himself in the position of either delivering the promised membership referendum or going down in history as yet another Prime Minister who failed to fulfil such a promise. Maybe the EU will undergo reform, but I suspect much of that would be window dressing and, at this point, any future reform comes too late for those who wish to make the case for continued UK membership. Horse, door, bolted.