It looks like your theme is putting all that space in there, so you may get a more detailed response from the theme support. The plugin mostly just lets the theme do the styling.
Since you’re using the browser developer tools to show the layout, you can also use it to figure out what CSS rules you need to use to change it. When you select an element, it will show you the CSS rules that are styling that element. You can use a similar rule with different values to change that because it will override the existing rules.
The plugin has a place for custom CSS in the settings.
For a more in-depth answer, take a look at this article that present a step-by-step method for figuring out how to make changes to the CSS.
Simple CSS Techniques for WordPress
For your buttons, there are two ways to go: if you’re technically inclined, you can set up a custom template that duplicates the HTML your theme uses…usually you just need to use the same class names that the theme uses in it’s standard elements.
Otherwise, you can inspect the element that looks like what you want the plugin buttons to look like, then add similar CSS rules to the custom CSS setting that target the plugin buttons.