inability to add properties to the second language

I can’t reproduce this on a simple setup, it may be you have a permalinks issue in which case this would be fixed via Settings, Permalinks and saving to force an update.

Please note the current release version 1.4.3 is rather old, a draft release has been created here addressing primarily variable product and variation issues and JQuery updates (props @leemon):
https://github.com/hyyan/woo-poly-integration/releases/tag/1.4.5

If there are specific outstanding issues on the latest version please report in as much detail as possible on https://github.com/hyyan/woo-poly-integration/issues