Yes, it is possible. Yes, it is a good idea (for all sorts of reasons, from simplifying management to SEO).
There's a load of plugins designed to do just that. Just search for "wordpress media library management plugin" in your preferred search engine and pick one that suits your specific needs.
The image sizes are set in functions.php and the theme will resize thumbnails and put them in the media folder. The theme will call different image sizes or thumbnails using a function call in the template.
Child themes may not show images the same and may not be centered. Themes use CSS to set the sizes of the image as rendered and there are lots of ...
WebP images load faster than JPG and PNG images, so it is a good progressive enhancement, particularly if your site is image heavy.
But if by "only" WebP you mean there would not be a JPG or PNG alternative, I don't think that is a good idea because your images won't be available to people on Internet Explorer, which doesn't support WebP right now.
If your AWS instance is just a storage node then you would need a processing server which can download the image, convert it, and upload it back to AWS.
If your AWS instance does more then you can use a backend programming language to make the conversions.
How are the images being uploaded exactly? If people are using FTP directly then you'll need to ...
Since you are posting on webmasters, I assume that your server is hosting your backend with some "web-based" language.
Since Nodejs seems the most popular, I suggest you to look at Sharp.
You can also use the Nodejs AWS SDK to make it in one script: documentation
As @Steve said, there is a lot of options here. You have to be more specific on your ...
The answer to your question is "yes".
Assuming you have your own custom site with your own code written in PHP, you would use something like https://imagemagick.org or https://github.com/free-open-source/php-image-converter (I have no connection - found by doing a basic search).
There are many other options, you would need to do your own research ...