Hello,
#1. Sorry, I have just fixed this issue, please recheck this button on mobile version.
#2. Yes, I have updated the main-theme to the latest version for you, so no need to worry about this.
About child-theme: all customizations are written in child-theme, if you update child-theme you will lose all custom code, so please do not update child-theme under any circumstances.
In short, when your website is working normally and stably, you do not need to update anything.