WordPress.org

Is the plugin compatible with 'WP Cache' and 'WP Super Cache'?

Technically, it is. But as it wouldn't be meaningful (with static HTML files not even possible) to let cached pages serve the dynamic archive link, 'Entries on page x' detects these plugins and serves a) a basic link to page x without category, tag, author oder date if you run 'WP Cache' or 'WP Super Cache' in legacy caching mode (»Half on« setting), or b) a link to the blog's home page only if you run 'WP Super Cache' in full mode.

If you use 'Super cache' mode permanently, is doesn't make sense to run the 'Entries on page x' plugin. But if you activate 'Super cache' only at high server loads, you can use 'Entries on page x' and don't have to worry about broken links.

Is the plugin compatible with 'DB Cache' and 'Hyper Cache'?

Yes, it is. (It is supposed to be.)