Hello, wpfed, & welcome. Those errors are actually likely not at all unrelated. For whatever reason, you’re getting database connection errors. These can be caused by a variety of factors–a database that’s too large, not enough memory, a site unable to handle the amount of traffic you get, a corrupted database, & others, as well as a combination of such errors.
Were I in this particular situation–& I have been in the past when diagnosing clients’ websites–I’d check to see if your hosting provider’s control panel has a page that lists most recent errors. Perhaps that might be enlightening. I would also browse through your WordPress folder & subfolders to see if you have any files called error.log or error_log. You can open those up in your hosting provider’s file manager or an FTP client, hopefully one w/secure file transfer capabilities to see if there are entries corresponding or in proximity to these errors. You may also wish to open wp-config.php in your file manager & change wp_debug from ‘false’ to ‘true’. Save the file, then do what you were doing to try to reproduce the error. You are advised that this poses a security risk, so change back to ‘true’ when you’ve finished. That might give you an idea, however, if a specific plugin or theme is causing the error. Sometimes it’s also helpful to try disabling all plugins & temporarily switching to a default theme (they begin w/the word ‘twenty’) to see if doing so resolves the error. If it does, then try reactivating the theme you had been previously using. If the site still works, then try reactivating plugins 1 by 1, each time doing what you need to do to reproduce the error, until the error recurs, at which time you’ve got a pretty good idea what plugin is causing the problem.
I would, in this situation, also go to your hosting provider’s control panel & run a check on your database. That may tell you whether the database is corrupted. There is usually also an option to repair it.
You may also wish to contact your host to see if they’re seeing any mod_security errors thrown by your site.
If you feel this is over your head, & your host won’t help, there is a job board at https://jobs.wordpress.net where you can post a request to hire someone who can help you. I was a bit disappointed you didn’t post a site url so I could have a look. It might also be helpful if you’d tell us whether you’re running shared, VPS, or dedicated hosting.