Hi,
What you said about the user creation gave me the idea that your issue might be linked to a major problem in your database.
So, after I checked I was able to somehow reproduce the issue on your products listing, I went to your orders listing. There, I clicked on the "new" button in order to create a new order. Normally, the new order should have the id "2" since there was only one order with the id "1". But the new order was created by MySQL with the id "0". This means that there is something seriously wrong with the database. The primary key and / or auto_increment must be missing in the hikashop_order table, and probably with all the tables, not only HikaShop.
I clicked on the "check database" button of the HikaShop configuration. The system found that all the auto_increment values and primary keys were missing in your HikaShop tables and fixed them:
i.imgur.com/DCsfVRP.png
After this, I'm not able to reproduce the issue with the ordering of the products. And the order creation process has been fixed too (and probably any other process of HikaShop which requires saving stuff to the database).
However, note that this only fixes the problem with the HikaShop tables. You likely have the same problem with other tables in your database, like the users table of Joomla, which would explain the error you have with the user creation.
I think this issue comes from a database migration issue. Something must have gone wrong along the way and the primary keys and auto_increments have been lost. That's a big issue. While the check database process can mitigate the problem for HikaShop, you likely want to go over the migration steps you took to avoid loose the primary keys and auto_increment of your tables in the first place.