I took a look at your site, but it's in Hebrew, and when I tried switching the user profile language setting to English (so it would affect me, but not the site language) the backend still appears mostly in Hebrew with some English and the layout is messed up.
Long story short, it's not so easy for me to check this.
This isn't a production site, no? Can I change the default site language to English while I investigate, or will that affect anyone looking at the site?
I did that and saw the issue with the term field group saving only its title and not the fields you add to it.
I quickly disabled the WPML plugins and switched to English to remove the possibility that the issue was related in any way to the language, but I saw the same.
I have reverted to Hebrew and re-activated WPML for now.
I suggest you try a no-conflict test—in whichever language you are most comfortable with—where you switch theme to twentyseventeen and check to see if it still happens, then disable all non-Toolset plugins and check to see if it still happens.
If not it should be possible to identify the source of the conflict by re-activating the other plugins one by one or in batches.