Internal Server Error and bad CSS

I'm currently working on a WooCommerce website that is facing a lot of Internal Server Errors and sometimes even bad CSS. An example of bad CSS:

The site loads like this at times, when it should load like this:

The site has the following plugins installed:

Akismet, Code Snippets, Mailchimp, Max Mega Menu, Nav Menu Roles, Pie Register, Virtue/Pinnacle Toolkit, Woocommerce, Woocommerce PDF Invoices & Packing Slips, Woocommerce Product SKU Generator, Wordpress Social Login, YITH WooCommerce Wishlist.

The site is hosted on a shared Linux server from here. It has about 1TB of memory and 5GB of disk space. The error log in cPanel shows the following errors, regarding the internal server error:

Cannot allocate memory: couldn't create child process: /opt/suphp/sbin/suphp for public_html/index.php, referer: [URL to the page trying to be opened]

Cannot allocate memory: couldn't create child process: /opt/suphp/sbin/suphp for public_html/wp-admin/admin-ajax.php, referer: [URL to the page trying to be opened]

I cannot understand if a plugin has some bad code hogging too much memory, or if the shared server is not able to take the load of the amount of plugins we have on the site.