I think you're pretty on-target here, but since you say you like debate, I think there are a couple of other explanations that shouldn't be totally discarded for Part I.

First, your argument explicitly relies on the premise that the difference between state-sponsored violence and interpersonal violence is (or should be, unless they're racist) obvious to the commenter. As support for this, you offer the effort that it takes to dig up stats...which would be a good argument if the stats themselves weren't a meme floating around the internet which can be referenced with nary a thought. So I don't think you can so easily reject the naive "a life is a life" feeling that people can have. With this feeling, and attention measured in seconds to a couple minutes, not hours of digging, the comment (in some formulations) is explicable without any reference to racism. (I haven't witnessed this for exactly this topic, but I have witnessed it for similar issues.)

Second, your argument implicitly relies, I think, on the premise that attention, political capital, and funding to solve societal problems are all infinite--which is not the case. Even granting that state-sponsored violence is worse per-death than interpersonal violence, it is nonetheless true that both cause suffering. Then the argument goes: by sucking up all the available attention, a focus on state-sponsored violence leads to increased suffering by draining attention away from solving interpersonal violence (and also by limiting our ability to use the power of the state to reduce interpersonal violence). Reduced to a tweet, the message is exactly: "BLM doesn't care about black lives because it ignores blacks killing blacks". One could argue whether this position is correct even given the wrong-attention perspective but it is not so obviously blatantly wrong that nobody could actually believe it, which is what would be necessary for it to necessarily be an indication of racism. (Indeed, in this view, BLM might be seen as (hopefully inadvertently?) racist against blacks!)

Now, in a long format, I don't think either of these would be hard to detect: the person would actually say some of the stuff above, which would allow one to distinguish the common "I need a rationalization to support my racist intuitions and this stat feels good for that" reason from the (putative, rarer) two above, which should be handled differently.

I completely agree with Part II. Maybe I'm missing something, but I just don't see any way to excuse this. (It's not as damning as the others either, but still.)

With regard to Part III, I think that when presented the way you characterize, the point has no redeeming qualities. However, your line of argumentation taken without any qualifications suggests that either black people have no agency to improve their condition, or that black people are flawless, both of which strain credulity. Otherwise in at least some contexts it's worth asking whether more can be done at an individual level...the converse of which is that if more isn't being done it is partly "black people's fault" (in a sense). However, in practice I at least haven't seen people raise individual empowerment (and its converse) in good faith while also matching your characterization, so I'm willing to provisionally accept the notion that this form of it always comes up as a rationalization for racism.

Anyway, I think for the large majority of comments, you're right on target. But recognizing when there may be an alternative might provide a path towards dialog and more effective action as opposed to further entrenchment. Furthermore, being a little more charitable than is warranted might provide a path for the weakly committed racist to start believing their reasons instead of their biases, and work their way to a less problematic viewpoint.

(Meta-disclosure: "Why is this person entering a debate on these things?" Answer: "Because being able to resolve differences through debate is central to achieving justice in a democracy, and if not applied with care, exhortations to automatically classify people as immoral based on superficial observations can make debate incredibly difficult. And, Quora happened to show me this one.")