He killed two of Graendal's favourite pets (and not with the TP, with his hands). There's no reason to believe they were DF.

As far as we can tell, and since Brandon mentions this in the context of the Elza episode, it's objects SH appears unable to move around.

We've seen him interact directly with people (DF and non DF), but haven't seen him interact physically with his surroundings or with objects other than living things.

Part of that may have to do with the fact he's part Myrddraal - at least it's reminescent of how their cloaks don't interact with the wind at all.