Hello M One and netdiva790,
Using a table would be a bit hard as you would manually have to split the links into equal length columns and then use two or more shortcodes in a HTML table in your page.
Using CSS you could make a template which displays every link as a list item:
<link_xxx_etc]</li>
The “before” template (in the plugin settings) would be
<ul class="three_column_links">
And the “after” template:
</ul>
You could then use CSS in your WordPress Theme CSS to display lists for the “three_columns_links” in columns, using the “column-count” CSS3 property: https://www.w3schools.com/cssref/css3_pr_column-count.asp
It should be supported by all modern browsers, but I have no experience with it myself.
About images, Yes, you can assign images to links in the Links module of WordPress. You can then retrieve the url for an image using the template tag [link_image].