If there is a poorly built plugin that hasn’t been updated in two years, and I make the poor decision to install it anyway – is it possible that even after complete deletion this plugin could still be effecting my site?
Yes, a plugin that does not properly clean up after itself can continue to affect your site even after deletion. It can leave stuff behind in the database, or make alterations to your .htaccess file, which is probably the case in your scenario.
I really need to think twice before downloading plugins like this.
There’s no catch-all method of tracking down DB changes made by a plugin – you’d need to study the plugin’s code to see what it was up to.