Going through this one by one:
Specifically I would like to (on category pages):Whether this is possible on a category basis is yet to be seen. It would require so much work that you'd need a professional site developer.
- change the featured image size to "full size", in this case about 600 px width (may vary between pictures)Go to Dashboard > Settings > Media and set the thumbnail/featured image size to 600px. Even if your images are larger, they would be cropped to that width. You may need to update existing images which may currently be resized by
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and use it with Firefox to locate the border CSS and remove the padding and set the border to 0.
- change the featured image link to the image url (rather than post url)This also should require the aid of a site programmer as it requires changes to the WordPress code OR, a specialized hook in functions.php.
- display the post title on the left side of the featured imageThis is a mixed message. You can't have both a full-width image AND the post info on the side. I see your demo image, and that's achievable also with a hook but not together with a full-width post feature image.
- display the post text on the left side of the featured mage (under the title)The post excerpt is designed to follow the post meta information. Via Dashboard > Settings > Reading you can select to use the full text rather than summary, which would place the full article there.
If you need a pro developer, I'd suggest
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