Hi @cdl, note that we are in the middle deprecating LME regression in favor of other differential abundances methods such as songbird and aldex2. See this post as well: Linear Regression Summary in Gneiss - #11
Concerning your other questions, y1 is the name of the log ratio. See the original gneiss tutorial on this Differential abundance analysis with gneiss — QIIME 2 2019.10.0 documentation
The coefficients are slopes (i.e. differences across groups) in units of log-fold change (also covered in the tutorial).
It's not clear how to compute R2 in LME, this is an open statistics question as far as I am aware.