Any log analyzer will tell you which path is the most hit. For slowest paths, I think a server daemon could theoretically log how long it took to serve the page

Any log analyzer will tell you which path is the most hit. For slowest paths, I think a server daemon could theoretically log how long it took to serve the page from request in to last byte out, but I don't know if any of them do that - you might have to set up a custom format for logging, and then from there you'd need to tell your analyzer how to interpret that field. For cache hits, I guess it'd depend on what sort of cache you have in mind, but that might be something you could only effectively log at the application level.