Hi,
First, there are several javascript errors on your pages:
i.imgur.com/l0rwqhB.png
This might lead to HikaShop's javascript not being initialized and then not working properly in some cases.
If I look at the lines pointed by these errors, they seem to come from the template/menu system you're using.
If the cart module is not being refreshed after an add to cart but that the notification popup works, this normally means that the add to cart worked, but either:
- the cart module's javascript didn't register to the add to cart system to refresh itself after the add to cart is done. This possibility could be checked by looking at the xhr requests in the network tab of the developer tools of the browser. if there is a request for the cart module to be refreshed, but that it returns an empty cart, then it means that it is not this possibility as the javascript is working fine. If you don't see the request for the cart module refresh, then that would indicate a problem on the server side, not the javascript.
- the user session was lost at the end of the add to cart AJAX request, so that when the AJAX request is done on the server side, the system doesn't see the cart anymore and thus it still displays an empty cart. That would also explain why the cart menu redirects you back to the products or the login form (based on the situation it will either think that the cart is not available because it is empty and thus will direct to the products listing, or it will think that the cart is not available because it is linked to a user account and the customer needs to login to access it).
I looked a bit at the situation with Chrome on my end, but I wasn't able to reproduce the issue. I suppose it's because I can't do the step "Go to admin > Log in to backend" since I don't have such an access on your website.
Did you check the issue on other browsers ?