Sure.
Yep, so first thing here is that anoxic conditions does not need to mean oxygen is bound in anything else. It can simply be where there is no molecules at all that contain oxygen. Anoxic conditions are just conditions that lack oxygen. The actual concentration itself varies depending on the field of research, but yes some fields define it as less than 0.5ppm (or mg/l rather, but basically same thing).
Ah, so yeah here is the problem. The science DOES matter because we are dealing with it, whether we want to or not. The statement 'heterotrophs requiring oxygen, that's seems to be the underlying element that allows nitrates to be reduced to nitrite' is wrong here. It's not because they need oxygen that allows them to reduce nitrate to nitrite. It is simply that a redox reaction is catalyzed via the electron transport chain, with nitrate as the terminal electron acceptor:
https://metacyc.org/META/NEW-IMAGE?type=REACTION&object=RXN-11236. I want to clarify this point because it is not as if the bacteria somehow pulls out the oxygen from nitrate first, prior to using that as a terminal electron acceptor. No, it is one direct reaction. It is also why phosphate is not used as a terminal electron acceptor (aside from the redox potential stuff), these organisms are not taking out oxygen to use it.
I mean, it is precisely because of concerns you raised that I talked about the HNAD bacteria. You did ponder 'how exactly are these same bacteria able to remove nitrates and phosphates in an aerobic environment where carbons are dosed'. Well, one possibility is via HNAD.
If you really do not care about the functions, then don't go around trying to explain how it works. It is fine to tell everyone you believe the first part of this quote, but not to try to explain the science behind it.
No you don't.
And I defined it for you multiple times already. Whether an organism is aerobic or anaerobic (or both, which we call facultative (an)aerobic) is dependent on what terminal electron acceptors they can utilize for their electron transport chain.
Then why refer to these microorganisms as 'autotrophs' and 'heterotrophs' anyways? Those are scientific terms, with scientific definitions. You can't have a foot in both camps.
Anoxic conditions are conditions devoid of oxygen (in O2 form), that's all there is to it. It can contain substrates containing oxygen, or not. But if it is devoid of O2, i.e. dioxygen, then it is anoxic. Anaerobic conditions refer to the exact same thing. When it comes to the environment, both terms are used interchangeably. The preference however is to use the terms 'oxic/anoxic' rather than 'aerobic/anaerobic' to describe environments.
Coolio.