“The issus seems to come from the header personalization when we are not using a pre-registered template from Xstore.” – please describe what you mean by that in more detail.
Also, please check how it works with a default WP theme, not XStore. Storefront is a default WooCommerce theme. It is important to check if the problem persists with the default theme to find out if it comes from the theme or from something else. Go to Appearance > Themes > install and activate the Storefront theme. Then test and let us know the result.
Widgets could be messed up after switching, so open the Appearance > Widgets tab before switching to be able to move the widgets to the correct area after switching back.
One standard license is valid only for 1 project. Running multiple projects on a single license is a copyright violation.