Our of your list, the only thing I put in the fridge is the stone fruit, grapes and sometimes kiwi fruit. everything else is usually left out on the microwave in the fruit bowl.
there is a pack of veg/fruit bags you can buy from the aisle where you find the clingwrap/alfoil/freezer bags, and it keeps your fruit and veg fresher for longer. I thought they were BS, but got some and think they are fantastic! They have extended the life of our fruit/veg when I use them. Must remember to get some more as I've run out!