Now I’ve got a link to a test page and some screenshots that are large enough for me to see, I can review this support case better.
My first observation is that the images are massive. Most are exceeding 4 MB. Some are larger than 10 MB each. There is no justification for needing such large images in a public facing website. So start by deleting these images, reworking them in your preferred image editor and then adding them to RapidWeaver again. I would normally expect each of these images to be less-than 1 MB, when properly optimised for the web. They only need to be about 2000px wide and saved at 80% quality. Free tools like ImageOptim or this service will help you strip-out all unnecessary image data to reduce sizes even more.
The download / Pinterest buttons are hidden on mobile or instances where a browser does not support the download attribute. We’ll also hide them if image links appear broken (or are taking too long to display). I suspect that is what is happening here, perhaps in part due to the huge file sizes.
The download button will only work if the images are stored on the same server that the webpage is hosted on. This is a relatively new security practice that the major browser vendors have recently introduced, and alas it isn’t fully documented yet.
Finally it appears your theme is not SSL compliant. It is trying to pull some fonts off Google Web Fonts. In some rare situations, a browser might abort loading a page fully if it detects insecure file calls or scripts.
The next update for ProGallery going out soon already includes some changes to how download and Pinterest buttons are handled within the lightbox.