1. The featured image is responsive so will size accordingly to the container width to a maximum of the original full image size. On rescaling the srcset images (thumb, medium, large) created by WP will kick in where applicable.
2. GP has a built in image resizer. Setting the sizes in Blog options will generate the image at that set size.
3. You could try this CSS to resize the Featured Post image:
Thanks for the explanation, that helped a lot. I tried using the CSS you provided but it didn’t seem to work for me. Regardless, I was able to do what I needed with the information you provided in #1 and #2.