I have looked at your ZIP file and I find the following things.
1. The file which you call font_test_notEmbeddedFont.pdf has all the fonts embedded. I don't know if InDesign will ever make a file without embedded fonts.
2. I don't understand why you changed the embedding percentage to 1%. The result was that the Dolly Roman font was embedded as a full font, not a subset.
3. The file with the full font does give an error message, in English it is "a number is out of range".
4. The problem seems to be with the Dolly Roman font. I suspect the font is faulty (though it could be an InDesign CS6 fault). Some unused characters have a huge width (65 ems) and this is a fault. You can avoid this by stopping any attempt to embed the whole font. There is today no reason to do this.
It does nothing to help editability; for this the person who wants to edit must own the font (fonts should not be shared with people who don't already own a license for them).