Hello,
Yes there are two options: you can upload just pages and you can uplod ready blocks from the template library.
In order to upload pages, you need to go to WoodMart > Additional pages https://prnt.sc/r6y3yh
If you want to upload ready templates, use our library: https://xtemos.com/docs/woodmart/templates-library/
As for So far so good, but the search-field was not working correctly
Please check the search settings in the Header Builder, check if it has been configured to search product or post if it has been configured correctly, but the problem remains, deactivate all the plugins not related to the theme and switch the parent theme, check the issue, if the problem remains, leave the plugins not activated and provide the site admin access to the private area
Best Regards