What to do after accidentally submitting to a "fake" conference?
First of all, it seems like a good thing you moved on. That does sound like a rather toxic research environment. Especially that:


  The abstract was accepted, the paper for the post conference publication submitted; but on the day of the conference I was told that my presense was not needed, and that the protocol of the conference was already being written, and my presentation was "discussed" and that I have answered all the questions. (...) I no longer work there. But, low and behold, on their site, where the publication must have appeared, in that conference there's not even a section to which I have submitted. My questions about the situation are unanswered.


That does sound quite shady. However, I am not even sure why they would do this. You do not mention having to pay something (and, honestly, if they asked for a registration payment or somesuch when submitting to an internal conference, you really should have turned and fled immediately), and I am not sure what other gains they would have from accepting and then silently discarding a paper. Maybe this was after all an ill-handled organisational issue - for instance, maybe they indeed planned to have this "special section" but did not receive enough submissions to hold it, so they decided to just never speak about the "special section" again. I am in no way saying that this is the proper way to handle such an issue, but I could see this happening in some places.


  Do I consider that particular paper published as a part of this conference? Can I reference it as published, since I was clearly told that it would be?


As I understand it, your paper did not appear anywhere. It is quite officially unpublished. You can not reference it (at least without putting it up on a preprint server or something like that), and I would definitely not list it on my CV.


  If I consider it to be unpublished, can I resubmit it somewhere else? Do I explain the whole situation during the submission?


Yes, you can (and should) certainly submit somewhere else. I see no reason to explain the situation during submission.

Let me re-iterate my main point. Your ethical concerns seem to stem from your understanding that this paper is "kind of" already published, and that submitting it again would be a double submission / self-plagiarism. In my understanding, this is absolutely not the case. Your paper was under consideration at another venue, but for one reason or another (does not even really matter why) it never appeared there. Hence, the paper is unpublished and you are completely free to do whatever you see fit with it. Essentially, the situation is the same as if your paper was rejected at the earlier conference. That they sent you an acceptance is not the important part, the important part is that your paper is nowhere published.