Maybe someone will have an use for him/herself in reading what I have learned:

- an n-gon is a face with more than 4 sides. sides means edges in this case, so even if one "side" of a face is perfectly straight, but split into 2 edges by a vertex somewhere along in it, it counts for 2, thereby making the face an n-gon (if all other sides are not split).
So, if I am not wrong you can only rid your mesh of ngons if you split all neighboring polygons of that specific ring/row as well. So, as a rule of thumb: If there is a vertex on an edge, both faces sharing that edge need to be split.

- my specific problem seems to have stemmed from accidents while extruding edges/faces; thank you MrYeti for pointing this out. These double faces also made it impossible to use the "fill hole" command on the hole shown in the images in my first post; after deleting the doubles it could be used.

- Thank you, Jay, for reminding me of working slowly, it really is of value to think more about what to do than just click along. Planning seems to pay off.

Questions still open:

-Poly with 3 sides are good/allowed?