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They (launcher of nuke) can use satellites to track their own missile and the interceptor.

Also separately, communication/radar works fine through reentry plasma once you go up to 20-50 GHz frequency.

My intuition says, due to the speeds and sizes of the two vehicles and latency of communications there'd be no way to figure out if the interceptor will successfully hit the nuke until it's too late.

If the interceptor misses the nuke's location by 50 microseconds it'll explode harmlessly a foot behind it. (The ICBM is probably traveling faster than the shockwave front of the explosive, depending on where it is)

I don't think a radar from satellite could be that precise, that fast, and get a signal out.

that sounds like it still adds way to spot the nuke and intercept it.

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