Seems like some misconfiguration in the shipping options to me, and is not a problem of Prestashop nor Magento.
You will have the same issue with Magento if you don't have enough knowledge to setup an e-commerce system, so don't blame the creators for this!
The shipping part is closely integrated with the warehouse part.
All products should be connected with a warehouse, and the warehouse should be connected with your shipping partners.
If you don't use the warehouse, you need to connect all products seperately to a shipping partner.
That means: big chance that something will happen like your problem.
Prestashop puts and get all data from it's database, so moving your shop from a sub folder to root folder can not cause any other products.
Perhaps something went wrong during moving your store.
Did you move the files to the root folder or made a fresh install in the root folder and then just moved the configuration file?
If you can send me PM with login for your backoffice I can have a look for you.
you can create an extra employee with my e-mailadres and some password.
Afterwards, just delete or deactivate my account.
BR,
Fabio