1a) I'm not really sure what you're asking - if you're using a difficulty selection, it'll naturally show the difficulties to select :)
1b) The node's help text says "during a running game", i.e. since you've started a new game and this is in your start game schematic, this is already in a running game and you should stop the game before calling the start menu (e.g. using Stop Game node.
Another alternative would be to use a completely custom start menu via dialogues in a schematic (e.g. started by an Auto Machine in your start menu scene.
2a) Hm, based on the images you don't have any Input Display set up for the button, so it doesn't actually visually display anywhere and is probably not getting any input (click).
2b) Should be same issue as in 2a.
3) No.
It has to be enabled globally for it to work and individual boxes can be excluded from it.
8/9) No, you'd put the text code for the flag icon (from TextMesh Pro icons, i.e. not an ORK text code) into a string variable, which you also put into the save file text. The save file text will have the content of the variable in it's text, which TextMesh Pro will output as the flag icon.
So all you need to do is have those icons set up in TMP as icons you can put in text, and have the text code for such an icon in a variable that's used by your save file text.
11) The start menu's auto save slot selection has an override question setup (part of New Game).
The Auto Save Slot dialogue in schematics also contains override question setup.
12) Ah, yeah - that's happening.
Will be fixed in the next update.
13b) The issue is not closing the dialogue - it's that you want to close dialogues from a different schematic via Close All Dialogues, which isn't possible.
The alternative setup was for making the 'exit game' handling as part of a choice dialogue instead of using a button with a schematic set up on the UI box.