How to interpret ANCOM results

For the second question - not quite. Here is an explanation of the percentiles. Note that there are pseudocounts, so all of the counts in the percentiles are off by one.

For the volcano plot, you are looking at the W statistic on the y-axis, and the F-score on the x-axis. So basically the x-axis is summarizing the effect size difference of the given species between your treatment groups, and the y-axis is the strength of the ANCOM test statistic that @colinbrislawn linked.

What you want to get out of this sort of plot are the ASVs with a high F-score and a high W-statistic – in other words points that are close to the the top right corner. These indicate that an ASV is suspected to be truly different across the groups.