SQL Database optimization & OpenCart fixes

We have an Opencart Website, with over 600,000 products. The backend of the website is very slow when searching, or preforming tasks, and the front end is slow when making searches using the search bar. We are also currently getting 500 Internal Server errors, and Fatal Errors; MySQL server has gone away, and it appears that we are constantly having queries that are filling the query queue. We need this fixed, as a priority, and then we will need work done to optimize the backend, and the front end. 10015092 | *****_ocart | localhost | *****_ocart | Sleep | 40 | | | 0 | 0 | | 10015093 | *****_ocart | localhost | *****_ocart | Query | 3 | Sending data | SELECT [login to view URL] AS category FROM ocet_category_description cd INNER JOIN ocet_product_to_category pc | 0 | 0 | | 10015121 | *****_ocart | localhost | *****_ocart | Sleep | 30 | | | 0 | 0 | | 10015122 | *****_ocart | localhost | *****_ocart | Query | 1 | Sending data | SELECT [login to view URL] AS category FROM ocet_category_description cd INNER JOIN ocet_product_to_category pc | 0 | 0 | | 10015197 | *****_ocart | localhost | *****_ocart | Sleep | 14 | | | 0 | 0 | | 10015198 | *****_ocart | localhost | *****_ocart | Query | 14 | Sending data | SELECT COUNT(DISTINCT p.product_id) AS total FROM ocet_product p LEFT JOIN ocet_product_description | 0 | 0 | | 10015213 | *****_ocart | localhost | *****_ocart | Sleep | 10 | | | 0 | 0 | | 10015214 | *****_ocart | localhost | *****_ocart | Query | 10 | Waiting for table level lock | UPDATE ocet_product SET viewed = (viewed + 1) WHERE product_id = '705235' | 0 | 0 | | 10015219 | *****_ocart | localhost | *****_ocart | Sleep | 7 | | | 0 | 0 |