What known comets are binary? Many asteroids are today known to be binary, to have "moons".

But what comets are known to be binary? Or what fraction of them are theoretically thought to be binary? And if possible, then separate Oort cloud comets from comets with more local asteroid like orbits in this respect.
None. and that doesn't surprise me much.

Comets are thought to be Oort-cloud objects which by interaction either with other Oort-cloud objects or with objects passing the Solar system have been perturbed to venture into the gravitational reach of the outer planets, whence they are
flung into the inner Solar system via close encounters (gravitational slingshots) with one of the outer planets, in particular Jupiter and Saturn. For such a slingshot to be efficient, the encounter must be close when any binary (proto-)comet will most likly be disassociated by the gravitational tides of the sling-shooting planet.