Magento – Add Image Thumbnail Next to Product Name on Grouped Products

If you're comfortable with editing the database directly, I can point you in the right direction.

SELECT * FROM catalog_product_entity cpe
    LEFT JOIN catalog_product_entity_varchar cpev ON cpev.entity_id = cpe.entity_id
    LEFT JOIN eav_attribute ea ON ea.attribute_id = cpev.attribute_id
WHERE ea.attribute_code = 'image' OR
      ea.attribute_code = 'small_image' OR
      ea.attribute_code = 'thumbnail'
ORDER BY sku;

That'll get you all of your products and all of their image attributes. Take note of which attribute has your values. You may need to look at catalog_product_entity_varchar directly to get the attribute_id of the other two image attributes (one of image, small_image or thumbnail, probably the latter two).

So you could write a PHP script that directly inserts into catalog_product_entity_varchar, using the results from the select statement above.

You can edit this template from your theme catalog/product/view/type/grouped.phtml and replace the sectnion that lists all the simple products:

     <?php if ($_product->isSaleable()): ?>
        <td class="a-center">
        <?php if ($_item->isSaleable()) : ?>
            <input type="text" name="super_group[<?php echo $_item->getId() ?>]" maxlength="12" value="<?php echo $_item->getQty()*1 ?>" title="<?php echo $this->__('Qty') ?>" class="input-text qty" />
        <?php else: ?>
            <p class="availability out-of-stock"><span><?php echo $this->__('Out of stock') ?></span></p>
        <?php endif; ?>
        </td>
     <?php endif; ?>

with this:

   <?php if ($_product->isSaleable()): ?>
        <td class="a-center">
        <?php if ($_item->isSaleable()) : ?>
            <input type="text" name="super_group[<?php echo $_item->getId() ?>]" maxlength="12" value="<?php echo $_item->getQty()*1 ?>" title="<?php echo $this->__('Qty') ?>" class="input-text qty" /> 
             <!-- [+]  add this-->
            <button type="button" onclick="setLocation('<?php echo $this->getAddToCartUrl($_item) ?>' + 'qty/' + $(this).previous().value)">Add to cart</button>
             <!-- [-]  add this-->
        <?php else: ?>
            <p class="availability out-of-stock"><span><?php echo $this->__('Out of stock') ?></span></p>
        <?php endif; ?>
        </td>
     <?php endif; ?>

I didn't test the code so there might be some errors bu this sounds like the way to go. You can work on the button styling and translating the add to cart text.