Related your point 1:

I even want local notes. Once I walked around with SCEE or Streetcomplete ... and I added a note. And then the note was public on OpenStreetMap. I meant it as a note to me, so that I later could fix the thing at my desktop computer with JOSM --- which is, for some things, way better than doing it on-the-walk with a smartphone, no mouse, no real keyboard.

Also workaround for 1: In OsmAND you can define your POIs, they are then stored in on the devices. And then you can use things like SyncThing to share them.