I was able to correct these problems by changing the code:
cart/showcart
from
<a class="hikashop_no_print" href="#" title="<?php echo JText::_('HIKA_DELETE'); ?>" onclick="var qty_field = document.getElementById('hikashop_product_quantity_field_<?php echo $cart->product_id;?>'); qty_field.value = '0'; <?php echo $input; ?> qty_field.form.submit(); return false;">
of
<a href="<?php echo hikashop_completeLink('product&task=updatecart&delete=1&quantity=0&cart_type='.$cart_type.'&cart_id='.$cart->cart_id.'&cart_product_id='.$cart->cart_product_id.'&Itemid='.$Itemid); ?>" title="<?php echo JText::_('HIKA_DELETE'); ?>">
and cart//showcarts you miss some code that does not allow to display icons
$userCurrent = hikashop_loadUser();
of
$userCurrent = hikashop_loadUser(true);
if(isset($userCurrent))
$userCurrent = $userCurrent->id;
else
$userCurrent = 0;
and
<?php if($userCurrent){ ?>
of
<?php if($userCurrent != 0){ ?>