You can absolutely do all of the above with a SSG. But unlike say Wordpress where you can get a lot of these features by installing a plugin, most you’ll need to develop yourself, at least in Jekyll-land.
Depends on your needs and you’re only looking for cheap or “free” solutions. Services like Cloudinary might be the way to go as they can host your images, provide them in various sizes via an API, multiple formats, and a bunch other neat things.
Will depend on how you’re referencing images in your content. If you have control over the markup via a layout or
loading="lazy" attribute to your images which latest browsers support.
Doable. You can use Jekyll plugins or write your own
_include helper that can loop through images defined in YAML front matter.
Will depend on the size of your site and how long it takes to build. Netlify caps out at 20minutes. Travis CI and other CI/CD services have varying build time limits. You may have to build locally then use something like rsync to push to server. I used to do this with Gulp tasks before moving to Netlify.
Depends on your needs and what you can get away with services that offer generous free tiers.
Will depend on the SSR you go with. For Jekyll not sure of any webp plugins, but you can use a task runner like Gulp to convert all your images for you.
For inspiration, this site has a lot of photography and nicely put together galleries. I believe he’s still using Jekyll to build it all.