Maybe you already know about these, they aren't free, but they do address your issues.

For number 1 there is: https://funk-isoft.com/display-maid.html or https://rectangleapp.com/pro

For number 2 there is: https://manytricks.com/menuwhere/

I think both should in some form be supported natively though. My reasoning for the second is that many apps are now using command palette search overlays when technically 'command + shift + ?' or even somewhat 'Move focus to menu bar' system option already does that. But because of large screens it should just pop over the focused window and unify this experience across all apps.