iSaumya on "[Plugin: Link Library] Need help so set columns of categories"

you want me to use shortcodes like [link-library settings=2] instead of [ link-library-cats ]

Yes, I think that's what you are already doing. Or am I wrong?

Also how do I create these shortcodes like [link-library settings=2]?

In link library general options set number of libraries to 3. Then in the library settings these will become available. Goto library 2 and copy FROM library 1 to transfer settings. Repeat for library 3. Then for each library set up the categories to show.

How do I decide which category will go under which settings.

I'd say alphabetical order and try to distribute the cats equally.

Is there no way to automatically arrange the categories in the 3 column design based on window width?

Keep your current structure and use css columns as in my first answer. Then you can simply use 1 library like you have now, but I think you cannot control how the elements wrap.

If I explicitly which category will be under which side, it might look on on my screen, but it would look very odd on bigger screen like smart TVs or small devices like smartphones.

Use media queries to set the width of .LinkLibraryCat. You can also float them, lower css columns, etc.

For the more advanced positioning you'd probably need a masonry plugin or something like isotope.