Demandred has been shown to be extremely observant. He noted Graendal's overreaction to the Choeden Kal revelation in Winter's Heart, and based on that made the connection that it was in fact no surprise to her.

He also noticed the plain gold ring on her little finger, and based on the fact that it was not consistent with the flashy nature of her other jewelry, made the connection that it was likely an angreal or other threat of some kind.

He also reasoned out Rand's plan at Shadar Logoth as soon as he became aware of the location at which the Choeden Kal were being used. None of the others displayed such a level of understanding at the time.

Graendal noted Moridin's flexing hand when he spoke of Semirhage, but did not grasp its deeper significance. If she noticed it, Demandred assuredly noticed it as well.

Additionally, Demandred knows exactly what took place when Semirhage was captured, down to the bolt of fire described by Mesaana, and no doubt he knows about Rand's loss of a hand as a result.

So the question is: Did Demandred connect Moridin's phantom pain to Rand's loss of a hand? Did he understand this to be the basis for Moridin's anger with Semirhage?

And if he made the connection - can he use this to his advantage? Perhaps he is now thinking along the lines of killing two birds with one stone when he destroys Rand?

For the record, I think Demandred WILL kill Rand. His single minded obsession in this regard has been built up too much for anything other than such a confrontation to take place.

Might this cost the Shadow its victory, when Moridin dies along with Rand, only for Rand to somehow survive by being transposed/transmogrified/translocated to a new body, as has been hinted at before?

We know Moridin won't kill Rand, because then he will die along with him. Alivia also needs to be involved somehow, but the anti-climax would be extreme if Demandred is not part of the equation during this pivotal event. It is the single most important reason he is even in the series. To kill Lews Therin, somehow.