ive had much better luck with outliners like dynalist (and previously workflowy) and its the longest ive ever stuck with a single system (maybe 5 or so years). i think the lack of any structure helps things a bit since it gives you more freedom to arrange things depending on the type of task.
with an outliner everything is a bullet point (or node). every node has an optional note section, and every node can have more nodes nested underneath it. thats basically all there is to it, but it means you can arrange things to be a basic a shopping list, or a project that holds many other sub nodes/folders, or if you were writing an article or a book you could have each node be a sort of a header/chapter description and then the content written in each note section.
ive found that rescheduling or tagging features in most todo apps just ends up being more work than actually doing the tasks themselves, so the way i organise my todo list now is by just using now/next/later nodes. i usually have a handful of tasks in the 'now' section, and maybe 10 or so in 'next'. when i run out of tasks in 'now' i move things up from next/later or if there are too many tasks in 'now' i move them to 'next'. the 'later' section is an unholy mess of things but it really doesnt matter because that section is collapsed/hidden most of the time so its not overwhelming and the search is good enough that i can pull something back up easily enough without having to organise anything or follow a system.
overall, the thing i try to remind myself is that i can only work on one thing at a time. its irrelevant whether there are 10 or 1000 tasks up next after the current one. the only thing i need to worry about right now is working on the most important task.
personally i dont get much out of marking something off the list or keeping a 'done' list. just actually completing the physical task is enough of an achievement for me.
about point #5. i would really love to see a solution to that. its the one thing that bothers me about my current setup. small tasks and chores are mixed in right beside big projects and sometimes i only want to work on one type and hide the others. the only thing i can think of its maybe filtering the list by certain words, or maybe the node content since small tasks are just usually 1 node, and projects have many sub-nodes. but its not always that simple either, so other than the only solution is to go back to tagging things.