1) Yes, I'm interested.

2) I suspect that the study of rhetoric is already fairly rationalist, in the sense of rationality being about winning. Rhetoric seems to be the disciplined/rational study of how to deliver persuasive arguments. I suspect many aspiring rationalists attempt to inoculate themselves against the techniques of rhetoric because they desire to believe what is true rather than what is most convincingly argued. A rationalist rhetoric might then be a rhetoric which does not trigger the rationalist cognitive immune system and thus is more effective at persuading rationalists.

3) From my point of view the only goal is success - winning the argument. Everything else is an empirical question.

4) Not necessarily. Since rationalists attempt to protect themselves against well-sounding but false arguments, rationalist rhetoric might focus more on avoiding misleading or logically flawed arguments but only as a means to an end. The goal is still to win the argument, not to be more ethical. To the extent that signaling a desire to be ethical helps win the argument, a rationalist rhetoric might do well to actually pre-commit to being ethical if it could do so believably.

5) I think the study of rhetoric can absolutely be rational - it is after all about winning. The rational study of how people are irrational is not itself irrational.

6) My feeling is that the answer is 'to a significant degree' but it's a bit of an open question.