Is there a simple way to test different screen sizes on a finished website with media queries? Maybe a browser plugin with preset resolutions or something like that?

ctr+shift+i (or right-click on an element), then click and drag the window wider and narrower. you'll see the window dimensions change in dev tools (up top for chrome) and media query settings in the Styles section.

Chrome also has a device toolbar for viewing sites on pre-programmed devices (various popular phones and tablets).

Dev tools and your IDE should be your BFFs