Hi,
1. Regarding the custom address fields missing:
I'm not sure why this would happen. Could you provide a screenshot of the settings of one custom field which displays and one which doesn't from the Display>Custom fields menu ?
2. Regarding the email confirmation field:
There is not an email and an email confirmation field on the checkout registration form of your website.
I went and check there and you have a translation override on the "username" text to display instead "email".
So you actually have both the "username" and the "email" fields displayed, which is normal.
Now what's not normal is that you don't have the username field on the normal registration form. I can only think that you removed it from the view file with a view override. Can you confirm ?
If not, maybe it comes from a view override from your template.
3. Regarding the name field:
Similarly the the "username" field, it's normal that you have it there and not normal that you don't have it in the normal registration form. There is again no option to remove that field from the registration form (there actually is in the commercial editions of HikaShop, but not in the Starter edition).
Actually thinking about the issue and checking the code, if you had activated the "simplified registration" in the "registration" setting while using the Essential edition or the Business edition and then downgraded to the Starter edition, this situation could happen as there is a missing check to deactivate the removal of the name and username fields from the normal registration form when using the Starter even if the option had been activated before. So maybe the difference is linked to this ?