Will it work with EWWWW Image Optimizer?

Hi,
Thanks for contacting us here about this extension.

Will it work perfectly with EWWWW Image Optimizer plugin?

As I've seen, EWWWW Image Optimizer plugin runs smoothly with WP Media Folder.

Can i assign only specific folder to a specific Author? So that Author can only use media library of that folder?

Yes, you can limit access by user/ user role. For more details: https://www.joomunited.com/documentation/wp-media-folder-documentation#toc-4-3-media-access

If i change the folder name, Will it also rewrite all media urls in that folder?

You are able to change folder name without any effect to URLs, because URL link doesn't contain folder name.

Hope it helps!
Regards,