Import My Maps from my Google account to OSMAnd app?

Google My Maps does have an option to export as a KML file. If you are using the "classic My Maps", then it is in the left hand sidebar, just underneath the title. There is a link for "KML". If you are using the new "Maps Engine", then look in the top left box, underneath the title there is a folder icon. Click on that folder, then choose "Export to KML".

For using the KML file in OsmAnd, and I'm not sure if it is possible to load it directly. If you want to show lines on the map, then you can convert it to a GPX track, eg using GPSBabel. Then copy it to the osmand/tracks directory, and enable it in OsmAnd by going to menu > Define view > GPX track. See How to view GPX tracks

For a more advanced map, you could convert from KML to .osm format. Then use OsmAndMapCreator to create a map in OsmAnd obf format. Some more details: Using KML files

It's possible with a few steps. Ashraf Fouad has written a thorough blog post with detailed steps on how to do this.

I've exported my own starred locations using the method noted as 1-a in the blog post using the online tool at http://gexport.somee.com/ . Ashraf noted that it didn't work for him but didn't note why. I (too) needed to do some tweaking to get the conversion tool working. This was likely because I had so many Google Bookmarks that it seemed to choke the tool.

What I did was I edit your exported Google Bookmarks file so that it only contained rows that had a location, the starred locations (and a few other locations that were in the bookmarks, IIRC). The way I did that was by first (after making a copy of the original bookmarks export file) opening the bookmarks file in a text editor, them cut-pasting all the bookmarks to my favorite spreadsheet application, then filtering all rows without the location identifier (.. can't remember what it is but you'll see it when you open it). Then marking those rows and deleting them leaving me with only rows with locations and copy-pasting those rows back to the bookmarks file. After this I was able to get the gexport.somee.com tool to convert my bookmarks into a KML file. And then converted to GPX and imported to OsmAnd.

No, OSMand does not have that feature, as far as I know.

I also think it unlikely that any other app will have the feature if Google has decided that their official app should not have it. It is their data (not yours) and their API, so they are free to decide whether to give access on Android.

Seems that the recent version 1.8.3 converts/imports from KML, but after many searches I still unable to do it. The clue is that feature would be in My Places.