The theme itself comes with a child theme bundled with it. Pls start from it and any customizations should be in the child theme style.css. The child theme will not be updated ever since it is just a template and example child theme for users to start with and hence any changes you make to the child theme should stay when you update the parent theme.
You should not lose any options you have set when you update the theme. Anyway, it is a good idea to export it through Option Tree tab and keep it as a backup just in case.
If you are having trouble with mobile devices, it is mostly styling issue (theme or any custom CSS you have used). Not much to do with hosting. Can you share the URL here (as a private message if you prefer)?
Hope this helps.