You have the Table Entry Card template activated. This template does not have a category drop down. None of the other free core templates do either. I see you have Excerpt Plus installed, activate this template, it has the category drop down.
The images, apologies about that, seem a bug has made its way thru testing. When a PNG was uploaded for an image, the image size variations and HiDPI (Retina) images are created/saved as JPG/s but the URL for the image is PNG which does not exist. I have found and fixed the bug. A bug fix release will be released shortly … as soon as I’m finished tracking down and fixing a few other bugs.
In the meantime, you could re-upload the images again as JPG/s and they display fine.
Again, apologies for the trouble.