When adding a new photo to wordpress post, you have have the option to select the size of the image like you can see here:

Is there a way to edit the size of these images? The max width an image can be in a post is 598px, so is there a way I can specify width 598px for any of these?
Is there a way to switch all previous posts from “Full Size” to whatever size has 598px?
You can set the various image sizes in the backend – Settings -> Media
There you can set Thumbnail, Medium and Large.
To regenerate all the image sizes again after they have already been uploaded and resized by WordPress using the old settings you would use the plugin Regenerate Thumbnails
Don’t be misled by the name of the plugin (which although technically correct from a WP point of view is pretty misleading I would say). The plugin regenerates all the image sizes, not just the thumbnail size. It doesn’t regenerate the original full size version of course, just the three sizes you set in the Media settings.
The plugin author confirms it here -> Regenerate all image sizes