Meanwhile one of my colleagues helps you resolve the matter, I see, from your screenshot, these are warning messages and shouldn't bring down the site. However, since these are being thrown (or output) on a page, it might affect the visuals, user experiences and functionality.
Please do the steps mentioned in this guide https://wpml.org/documentation/support/debugging-wpml/, to log these into a file, instead of showing on the pages. And then share the file with us for a detailed investigation.