Internet Explorer And Formating

Start by sorting out the markup errors. Then move onto the CSS errors.
https://codex.www.ads-software.com/Validating_a_Website
If you continue to have problems with IE, consider conditional comment CSS

Dang, this is kind of beyond my scope of practice! All this coding stuff is kind of intimidating, is there not a plug I can run that can clean it up?

You could try https://www.ads-software.com/extend/plugins/tidy-up/ but ultimately, this is a hands-on job.

Thanks for all your help.

How does stuff like this happen, and what can I do to avoid it in the future?

I’m a Joomla guy, so this wordpress stuff is new to me.

It’s usually a combination of bad markup in the theme template files, the actual content of the Post/Page and/or markup added by plugins. That’s why you won’t find a plugin that will fix all of it. The range of possible sources is just too wide.