I would like to offer you some ideas for your questions 1 and 2, but I don't think I can. Family meals can be extremely stressful! And every family is so unique! In the last few years I have found a way round a couple of my family ideosyncracies, but there are still lots left!
However, I can make a suggestion on your third question - the shopping.
We do our main food shop online, and have the food delivered. I love it. Is that something you could set up?
The closest, largest supermarket to us is a Tescos, so that is what we use, but frankly I would use any of the big ones.
There are a number of different options for the delivery, from a flat annual fee to paying for each order. And the prices vary according to the day of the week and the time of day. It can be a very economical arrangement, especially if you factor in the cost of transport, buses or petrol.
I know that you like to shop daily, to prevent having too much food in the house, but would it work for you to have a delivery of the heavy stuff, or foods you are less likely to binge on? Meat for the freezer, pet food, bottled water, that kind of thing. Then you can pick up individual items daily, without having to depend on family for transport.
Hope that helps.