In addition to answering my first two questions in your first paragraph, your mention of feature definitions was a lot more helpful than answering the rest of my questions. (I'm not sure what I expected to gain from having the answers to those questions.)
Have a look at the element template for the points that are being annotated correctly, and compare them with those that aren't. I think you'll find that the points receiving annotations have an element template that has something under Point Settings. I suspect that those that aren't receiving annotations do not.
In my workspace, I see an Active Points field with the value 'X'. You may have a different situation. My understanding is that that is an anchor that annotations need. Apparently having a point there isn't enough.
The following screenshot may be redundant for you, but for others, I've highlighted the Active Points field that I'm referring to, and the way to add point settings in case your element template doesn't have an entry.
I hope that helps and solves your problem.