My understanding, and this article seems to agree, that the information about the asteroid (size, shape, composition) was not precisely known, and nor was the exact point of impact (as the ship was autonomously adjusting its flight path as it approached).
That’s exactly the point, some of the energy went into blowing all that material out into space, rather than deflecting the asteroid. A large point of this mission was to tell how much of that energy would be lost.
I’m not sure what you are defining as “head” and “side” for these purposes.
That’s not how it would work. It can’t add to the speed difference, as that would violate momentum conservation laws(unless it hits and releases a pocket of gas or something, but I think that’s unlikely enough to be ignored). Best case scenario would be a perfectly rigid collision where all the DART’s momentum is transferred to the asteroid. Any deformation of the asteroid would reduce that transfer, and anything blown off the asteroid would be using energy that is lost to deflection.
Ohhhh ok 
I can see how that would have been likely the largest question mark of the mission.
I said in another thread that maybe the unexpected extra change was due to this target being a rubble pile. I think their next test target should be a more solid body.
Ultimate goal? You want to know NASA’s ultimate goal? Behold!
http://j.aufbix.org/plif/archive/wc191.gif
We can’t really tell if things are a solid body or a rubble pile till we get up close, but the bigger a body is, the more likely it is solid.
This was a good test, as it was a fairly small asteroid orbiting a larger one. That makes it much easier to tell how much was imparted.
I would think they would next try to hit a larger asteroid.
Sure, but it really does need to be an asteroid in orbit of another asteroid, that’s really the only way we can get any level of accuracy as to how it was affected by the impact.
I thought they would predict the path, smack it, and predict the path again.
How much did the path of t he center of mass of the two change?
My understanding is they can’t actually see Dimorphos as a separate body from Didymos, the asteroid it’s in orbit around. The two are too close together to separate by telescopes on Earth. But since they are an eclipsing binary, they can determine the orbital period by measuring the brightness changes as the two orbit each other. So what they’ve found is that the period of the orbit decreased by about 32 minutes after being DARTed.
How did they know it is two masses?
Observation of the light curve, confirmed by radar.
The DART mission seems to have been unexpectedly successful at changing the orbit of this object; I don’t know why this is, but if the impactor hit dead centre, and penetrated sufficiently well to form a deep, conical crater which then funnelled the ejecta directly backwards, then the tiny asteroid would have briefly become a kind of rocket with nearly all the impacting energy pointing in one direction.
Contrast this with an impact that only formed a shallow crater - some of the momentum would have been dissipated sideways and effectively lost.