1. Your first point illustrates perfectly why the EU has turned this country's politics into such a mess. We haven't been given any choice on this fundamental issue since 1975 and that denial of choice or political diversity on the subject has built resentment, not lessened it. 82% of the populace (including 80% of Labour voters) wanted a referendum on the Lisbon Treaty, but Labour ran away from its promise to deliver one because it knew it'd lose and lose heavily. That sowed the seeds of Brexit. Had there been a referendum on the Lisbon Treaty, there's a strong case for saying Brexit would never have happened. In other words: that democratic deficit has brought us to where we are now. Moral: deny the people a voice at your peril.
2. There is a mandate for getting out of the EU. The nature of that withdrawal is a matter for the politicians and their success or failure will be judged by the voters. However, what is certain is that there is NO mandate whatsoever for remaining in the EU.
3. I know no such thing and neither do you. Some voted to remain because they actually believe in the happy horsesh1t about ending the nation state and subsuming ourselves within a Federal Europe. Others because they didn't like the EU but were worried about the financial impact of leaving. Others still because they believed the lies about the EU not seeking to create an EU army or because they didn't like Nigel Farage; or because they liked Mr Siddiqi next door and didn't want to vote with the nasty Brexit racists; or because they believed the stuff about the sky falling in on June 24th; or (in the case of my parents - which they now regret) because they thought it was a decision for younger people and younger people seemed to want to stay in; or because they work abroad a lot and the EU suits them; or because, or because, or because...
In other words, a multiplicity of reasons - just the same as Leavers. For you to try and claim 'they all just wanted things the same' with no nuance is exactly the same as me saying 'they all voted to leave the EU' - it is what the referendum was about, but it ignores individual motivations. However, what is clear is that on neither side does the fact that there was a range of reasons for voting justify ignoring their vote.
4. You simply aren't able to drag yourself away from the poisonous paradigm that millions who voted for Brexit were stupid and believed in a land of milk and honey. They didn't. They just wanted to get out of the EU and many of them felt they had nothing to lose by doing so. Again, however, there is no reason to ignore their vote.