Magento 2 Base URL – How to Get Base URL in Admin Static Block/Page

The way you are doing it is correct.
The {{store}} directive should know how to generate the correct link even if you change the customer module route name (that is currently customer). If you change it to client (see here how) <a href="{{store url='customer/account'}}">My Account</a> will still generate the correct url.
For CMS pages you should use the widget approach so it won't be important if the page changes.

{{widget type="cms/widget_page_link" anchor_text="some text here" title="some title here" template="cms/widget/link/link_block.phtml" page_id="52"}} 

Try this. I'm also not sure you need need to create a widget with that block. Although, I've personally never created a widget. You would need to put the block code within the <referenceContainer name="footer-container">

<block class="Magento\Cms\Block\Block" name="social_media_block" before="footer_links">
  <arguments>
     <argument name="block_id" xsi:type="string">social_media_block</argument>
  </arguments>
</block>

From how I understand it, since that block is something you created and not exactly an out of the box block that comes with Magento, you can't move it. That's just how I interpret it from my understanding.

And the arguments are necessary, else the system won't know what static block to pull.

Also, you can always echo the static block you created in a .phtml file like so:

<?php echo $block->getLayout()->createBlock('Magento\Cms\Block\Block')->setBlockId('social_media_block')->toHtml();?>

Good for if want to customize the layout of the footer.phtml file or something.