Hi,
The issue is with your template.
I just made a test on your website. After registering, I get redirected to the activation page correctly.
There, HikaShop displays the activation message, through the Joomla messaging system.
However, instead of displaying the message above the main area on the page, your template displays it on the bottom left area of the page:
i.imgur.com/JyeFOhZ.png
So it's easy to miss for the user.
Also, I didn't receive the email with the activation link for the user account.
It seems there is a problem with the email sending on your website.
Note that the account activation is something you can turn off in the Joomla user manager's options page.
Usually, on online shops, it's better to turn it off to provide a smoother checkout experience for users.
Finally, as you can see on my screenshot, I did try in English, and I didn't lose the menu on that page.