The language one is interesting. When I watch (say) Troy, clearly the characters are talking to one another, and in that sense the dialogue is diegetic (cf, say, Orson Welles' narration in The Magnificent Ambersons).Suppose that I am a man and english speaking, and my character is a woman and sylvan speaking. We take my human male-voice english-language speech acts to be (say) elven female-voiced sylvan-language speech acts. They're evidently not, but they do supervene. My character surely does not experience my english-language wordings.
But am I to suppose that they are talking in English, or in Homeric Greek, or in some earlier dialect of Greek?
I think I first consciously encountered this question watching films set in World War II, where some of the characters are clearly, in the fiction, speaking in German, but in the performance are speaking in English. Presumably it also arises in Star Wars, but I didn't think of it as an issue for that film until some time well after I viewed it.
Different films obviously handle this differently - I have a memory of one film, maybe with Jimmy Stewart in it (though my memories could be getting confused) in which the opening scene has a poster or newspaper in a Central European language but then it blurs into the same thing in English, an indication that we the audience are to treat English as standing in for whatever language the characters are "really" speaking.
Less sophisticated is, say, Hogan's Heroes, where I really don't think there is a way to make sense of which conversations take place, within the fiction, in English and which take place, within the fiction, in German.
RPGing uses a variety of techniques here. Your example is analogous to Troy, and so I think the dialogue is best regarded as diegetic, although rendered by the performers in a language other than the "true" fictional language. On the other hand, when the GM says to the players, none of whom is playing a PC who speaks Orcish, "The Orc addresses you in gruff tones in a language you don't understand" we have non-diegetic narration.
Some of the most thoughtful advice on non-diegetic RPG narration, in my view, is found in Vincent Baker's relatively brief GMing advice in In A Wicked Age.
Your action declaration is player-side non-diegetic narration. As I said in my post that you replied to, the player's statement "I jump" or "I fly" is not a diegetic event.I say that my character Jo jumps. I should think that Jo experiences jumping, but Jo surely doesn't experience my saying that Jo jumps. Therefore my capacity and acts as player in that regard are no more diegetic than if I rolled dice: both represent something in world without being that something.
The narration represents something in the world only in the sense that it describes it, as a particular instance of the general phenomenon of using language to describe things.
Rolling dice, on the other hand, doesn't represent in the same way. It's not a description of anything, nor some other sort of natural or non-natural sign of any imaginary thing. The outcome of the roll is a number, which is a sign. Whether or not it represents anything in the fiction will depend on the details of the RPG being played.
I think the relationship you are looking for is is a sign of, not is in a supervenience relationship with.Thus I'm speculating that any game element that has a supervenience relationship with stuff in game world can be said to be diegetic (or more accurately, I'm agreeing with your earlier intuition that it isn't a useful term.)
And this makes a classic D&D saving throw "non-diegetic" in your derived sense: the number on the dice is not a sign of anything in the fiction; it is just a number to be correlated with a chart to steer the ensuing narration.