Hi,
Would it be possible to have more details about your Joomla menu configuration for the "inscription" ?
Please provide a screenshot of your menu configuration in order to check the Joomla access levels.
Please also check your Joomla configuration for the User Registration.
I don't see any "Don't have an account?" in your first screenshot ; so it is possible that in the "Users" configuration you do not authorize the user registration.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.