Speaking generally, yes. Consider just the three body system of the Sun, Didymos, and Dimorphos. Despite the huge difference in their masses, Didy and Dimo revolve about their mutual barycenter – like the Earth and Moon, or Pluto and Charon, or even the Sun and the planets. This barycenter follows an elliptical orbit around the Sun.

Perturbing Dimo's orbit, by changing its mass, and its average distance from and period around Didy also changed the barycenter of the system. Therefore the impact on Dimorphos did change the heliocentric orbit of the Didy-Dimo pair. But in the real multi-body universe, the extent of this change is infinitesimally tiny compared to all the other forces constantly tugging on the Didy-Dimo system.

Undoubtedly yes, but that's MUCH more difficult to measure.

Gravity pulls on each other, just because it has a smaller amount of gravity doesn't mean it doesn't affect it. The moon moves our tides so knocking the trajectory of one would probably affect the other.

My understanding is the only measurable effect on the pair is Dimorphos's orbit around Didymos is slightly changed (well really they are both moving around the center of mass but I don't know where that is). I don't think their orbit around the sun has changed.

We aren't even sure that the orbit of Dimorphos has changed, yet (observationally). We won't know if Didymos' orbit has changed until we can assess the impact on Dimorphos, but all of our theories say that both orbits should be different now.

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