How to have a gallery in which each image’s caption is a whole “post”?

Uploaded images are already posts, a gallery is just a list of post IDs with some display options

In WordPress, when you upload an image it creates a post of type attachment, and these posts have URLs, templates, etc

If you just link the gallery items to their attachment page rather than the media file you’ll see this page.

Then, you can add an attachment.php to your theme, or even drill down to image.php etc. It might even look like the FB album you wanted if you code it that way.

Since attachments are posts, they can have comments, post meta, etc, just put your analysis in the description rather than the caption.