Hello,
1) What icon in the menu do you want to change? Provide us with link to your site and screenshot with the icons you would like to change for better understanding.
2) Yes, that’s could be the reason of the issue if you changed template name in the child theme style.css file to something else than xstore https://prnt.sc/1skikfm
You can change child theme name, child theme text domain, child theme folder name but the template should be xstore if the parent theme folder name is xstore. And don’t change the parent theme folder name because auto-update won’t work.
Regards