You will want to do this via default.xml. Ideally:
Here we will call on the minicart element and move it to your nav section or where you'd prefer, ex.
<move element="minicart" destination="top.links" />
Then we will want to go into the respective template file in my case top_links.phtml and we will call on the childhtml so we can render our cart like so:
<?php echo $this->getChildHtml('minicart'); ?>
The same will be done for the search.