Demo content installation should not overwrite/delete your data, it just adds new info. Likely Brands in your old theme is a custom taxonomy or custom post type (not the default WooCommerce option) that can be displayed only when that theme is activated.
To test it you can temporarily disable our Core plugin, activate that old theme, and check.
Widgets could be messed up after switching themes, 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.