Site going down due to slow queries

Perhaps info on this page might help: http://codex.wordpress.org/Class_Reference/wpdb

Other than that I would do the usual troubleshooting to start.

Backup everything.

Turn off all plugins.

Switch to a standard WordPress theme like 2015.

Then see what errors you are getting now that you have stripped down your install.

Then slowly turn things back on until you isolate whatever is troublesome and get rid of it.

If you’re convinced your code is sound look at a VPS, dedicated server, or a premium WordPress host as it could be a memory or resource issue you have run into.

You may also want to verify, your site isn’t under attack or have some malicious code wreaking havoc.