How identifiable are human omics data and how to mitigate their identifying features?
This is one of the major problems with genomic information in todays research. This was highlighted some years ago with the police using publicly available genomic data bases to idenitfy unkown murder suspects.
The full extent of this issue was exemplified in a
paper by Yaniv Erlich from 2018 that should be a good starting point for you.
They claim that giving the current (2018) amount genetic information more than half the searches for a person of european descent will result in a thrid cousin or better match. And these odds will only inprove with time.
Therefore, the genetic information not only can give you a hint at inherited variables like the approximate height of a person but can even yield their name and address.
About your second question, I would think that the amount of host (i.e human) material collected alongside the microbiome sample is rather small. This probably is not sufficient to obtain enough coverage for a profile. But I could be mistaken.