Product description on variants incorrect

It's working fine or our end.
Did you change anything in the product page's code ? Maybe it comes from such modification ?

The "error" in your browser means that a form was submitted in the previous page and that the browser has to ask again fo the page on the server. It should normally tell you to refresh the page.

Ah yes. For the product name, that's indeed the case.
We had requests to keep the main product name when you first reach the product page instead of displaying the variant name.

You can change the line:
if (hikashop_getCID('product_id')!=$this->element->product_id && isset ($this->element->main->product_name))

to:
if (false)

in the file "show_default" via the menu Display>Views if you don't want that.

For the "Document Expired", you will have the problem on the demo website too (I have it). That's because the pagination system uses POST to send the pagination changes and keep the URLs clean. We could send the pagination changes using the GET but the URLs would contain the pagination variables data, so instead of:
demo.hikashop.com/index.php?option=com_h...ng&Itemid=70&lang=en

you would get:
demo.hikashop.com/index.php?option=com_h...bd8a4b8bdf=1&lang=en

As URLs text is more important than the back button we preferred to keep it like it is actually.

We can't do much in HikaShop.
What you can do is add that line of code at the beginning of your joomla's index.php file:
<?php session_cache_limiter('private_no_expire'); ?>

That will ask the browser to not expire pages and should hopefully "fix" the problem.

Then, you will have to change all the method="post" to method="get" in the view files of HikaShop.
For products listings it's in the files listing_table and listing_div where you will find that on two different locations for the listing_div view file. You can edit them via the menu Display->Views.
You will also have to add the parameters of the URL as hidden fields inside the form, like that:
<input type="hidden" name="cid" value="<?php echo reset($this->pageInfo->filter->cid); ?>"/>
<input type="hidden" name="ctrl" value="product"/>
<input type="hidden" name="task" value="listing"/>
<input type="hidden" name="option" value="com_hikashop"/>
<input type="hidden" name="Itemid" value="<?php global Itemid; echo Itemid; ?>"/>


That will "fix" that behavior. Otherwise, you should see with your hosting company if you can force the non expiration of the forms with a modification of the configuration of your PHP/apache settings.

Yes, you can open the product page in a popup. Here is a thread where we talk about that:
www.hikashop.com/en/forum/2-general-talk...n-popup-product.html