No, it does not. Two species can evolve convergently irrespective of whether or not they are reproductively connected. They evolve in that the distribution of their genotypic and phenotypic features is different in one generation than it is in some other generation, and their evolution can converge in that the feature sets between the two species may be more similar between some pair of points in their history than between some other pair of points in their history. Jargon is not a political toy. Calling this phenomenon convergent evolution is not an expression of a commitment to any particular scientific model. It is a good name for it, because it correctly states what the thing is with words the etymological roots and meanings of which have been stable for thousands of years. There is nothing objectionable about this name.
I cannot begin to imagine how it would be even possible to do that. “Random”, as I said, and as you keep ignoring, is not a statement. So it cannot serve as a null hypothesis or any other kind of thing that would require it to first be an actual statement.
No, it does not. “Random” is a word we use to describe occurrences that follow less than entirely deterministic rules. Nothing about that word “supports” any statement about reproductive relationships.
Again, I have no clue how one could. “Divine creation”, as I said, and as you keep ignoring, is not a statement. So it cannot serve as a null hypothesis or any other kind of thing that would require it to first be an actual statement.
No, it will not. It is not a null hypothesis’ job to “bring a competing hypothesis in the mix”. Holding the door open for favoured conclusions is not what statistical hypotheses do.