Hello,
1) Cache plugins has option to disable cache for the site admins. That’s why if you are logged in you see uncached version of your site.
2) I disabled the Masonry yesterday. It’s not related if you are logged in or not or to cache.
3) All I can do for you, in this case, is set 100% for the mentioned images but then they will be blurred a little bit when the image block is bigger than the image. So, decide for yourself.
4) 245px width. Also, I would like to recommend you TinyPng service https://tinypng.com/ for image optimization, it’s really good.
Regards