1. Regarding the no registration checkout, yes you'll need a commercial version, you'll probably find more information
there
:
If you want to have a checkout without registration but with address, you will have to have both "login" and "address" views in the checkout workflow. Then, in the Checkout tab of the configuration, you can change the option "registration" to "no registration" in order to remove the creation of a user account. Also, you can turn off the "login" option there to remove the login area of the checkout.
That way, you will still have the address form but no user account would be created.
That "Registration" option is only available in our commercial editions.
2. As it's said on the documentation :
The fields layout enables you to ask your customers additional information thank to custom fields on order. This custom fields functionality is only available on the Business version of HikaShop
3. Can you show me how did you configured your address_state custom field, did you edited it ?