For rPHG - range_count is the number of reads mapping to a given reference range. taxa_count is the number of those reads mapping to a specific taxon in the range.
For the _attionalMappingStats files, they are just counts of some of the mapping statistics coming from the BAM/SAM files. 'count' is the number of reads which hit a given haplotype. 'totalNM', 'totalAS' and 'totalDE' are the cumulative sum of the NM, AS and DE fields in the BAM/SAM file for a given haplotype.
Finally listOfStartPos are the alignment start positions for each read with respect to the haplotype. Basically it allows you to look at how the reads are distributed along the sequence of the haplotype.
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A small educational note: if an answer was helpful, you should upvote it; if the answer resolved your question, you should mark it as accepted. You can accept more than one answer if they all work. If an answer was not really helpful or did not work, provide detailed feedback so others know not to use that answer.