...but the 'breath body' is not given pride of place (your "within the context of breathing as a 'body'") in step 3...
...In other words, in step 3 any remaining physical impacts are integrated into what was awareness of only the breath in steps 1 & 2.
This integrative step is what allows step 4 to be enacted.
The depth of experienced insight, as described, is tremendous; since samatha and vipassana here occur in tandem, I rather think this is to be expected in connection with Tetrad IV, and not step 3 in Tetrad I.
I do not think there is any support for this. The demarcation between "he knows" and "he trains" appears to me simply to be an indicator of the difference between a relatively passive awareness of the breath (1 & 2) and a more active application of the mind (3+).
I think the whole of anapanasati (sammasati) is preparation for samma-samadhi (jhana).