Objective morality as a proper basic belief

[The Grand Nudger]

I think alot of the confusion arises with the use of the words right and wrong in this context.

Agreed, but you aren;t going to be the one educating, on this count.  You;re in sore need of an education.

If objective morality (OM) does not exist, then the words are being used naively and incoherently. It doesn't make sense. What do i mean by this?

It means exactly what they've said.  Regardless of whether or not a person thinks that some act x is wrong according to some objective morality, or because that;s a consequence of their subjective morality...they are telling you that it's wrong.  

The words right and wrong ONLY exist in relation to facts.

That's borderline crazy.  The words exist even if moral facts of any matter don't..even if morality is entirely subjective.  We're both entirely capable of considering each other's fact free opinions wrong.

A fact is something that is true or exists REGARDLESS of anyone's opinion, preference, taste or desire.

Sure, and the fact of the matter in a subjective moral assessment is that person a thinks x is wrong, regardless of anyone else's opinion, preference, taste or desire.  

Let me use some examples.
It is a fact that the earth rotates around the sun. It does not matter what i or anyone's else's opinion, preference or desire is, the earth rotates around the sun. If i said the sun rotates around the earth, then i am wrong. I am only wrong because the statement was in relation to a fact.

If i sat an exam, and the question asked was, "does the sun rotate around the earth" and i answered with "yes", then i would get a cross. Would i get a cross because of how the examiner or marker feels? There preference? Desire? No. They would give me a cross because they would compare my answer against the FACT.

If i said chocolate cake tastes better than carrot cake, i am neither right or wrong because it is not a fact that chocolate cake tastes better than carrot cake.
Suppose you sat an exam and the question was asked, "does chocolate cake tastes better than carrot cake?" Well, if you said yes, will you get a tick or a cross?
Well, you wouldnt get a tick or a cross, because it is not a fact. There is no fact if chocolate cake tastes better than carrot cake.

Suppose you said yes, and somehow you get a cross, well you would immediately see the marker or examiner. How could the examiner justify giving you a cross? Suppose they said carrot cake tastes better than chocolate, but you prefer chocolate cake over carrot, then who is right or wrong? No one.
You cannot give a tick or a cross.
This is because taste in food is subjective. The words right and wrong cannot be used in relation to non facts.

Equivocative use of the word "wrong" is only an example of why you can't accurately summarize others moral positions or moral agency.  It's an example of why -you- are wrong...but not...case in point.....in any moral sense.