Magento – Magento 2 | Mini Cart has items but cart is empty | Session problem? | Double clicking on “Proceed To Checkout” redirects to an empty cart

on RWD default/template/checkout/cart/mincart/default.phtml line 158 replace this

            <a href="<?php echo $this->getAjaxDeleteUrl() ?>" title="<?php echo Mage::helper('core')->quoteEscape($this->__('Remove This Item')) ?>"
               data-confirm="<?php echo $this->__('Are you sure you would like to remove this item from the shopping cart?') ?>"
               class="remove">
                <?php echo $this->__('Remove Item') ?>
            </a>

with

            <?php if (strpos(Mage::helper('core/http')->getHttpReferer(), 'checkout/cart') !== false) { ?>
                <a href="<?php echo $this->getDeleteUrl() ?>" title="<?php echo Mage::helper('core')->quoteEscape($this->__('Remove This Item')) ?>" onclick="return confirm('<?php echo Mage::helper('core')->quoteEscape($this->__('Are you sure you would like to remove this item from the shopping cart?'), true) ?>');" class="btn-remove"><?php echo $this->__('Remove This Item') ?></a>
            <?php }else{ ?>
                <a href="<?php echo $this->getAjaxDeleteUrl() ?>" title="<?php echo Mage::helper('core')->quoteEscape($this->__('Remove This Item')) ?>"
                   data-confirm="<?php echo $this->__('Are you sure you would like to remove this item from the shopping cart?') ?>"
                   class="remove">
                    <?php echo $this->__('Remove Item') ?>
                </a>
            <?php } ?>

this will refresh cart page when you delete item from minicart

You can use the cart helper to check if shopping cart is empty.

protected $cartHelper;

public function __construct(     
        \Magento\Checkout\Helper\Cart $cartHelper
    ) {
        $this->cartHelper = $cartHelper;
    }

and then you can add your logic if the cart is empty

   if ($this->cartHelper->getItemsCount() === 0) {
          //add your logic 
   }