I think at this point, Strawberry Perl is the one to go with. While historically vanilla perl was more up to date (due to simplicity in testing a minimal bundle) that's no longer an issue and vanilla perl appears dead.
I have significant experience with Strawberry Perl (and before that Vanilla Perl) and so here's how it fits into your bullet points.
The library (single JS file) and examples can be found here: https://github.com/lagodiuk/earley-parser-js
Take a look at Komodo IDE. It has Perl support including a graphical debugger, a regex debugger, and code refactoring. If you don't need the debugging and refactoring capabilities, try Komodo Edit. Komodo Edit is a free version of the Komodo IDE with fewer features.
See the redbook entry on hooks for more information and the config ...
I believe it is difficult to answer your questions, because it really depends on your needs. How will you use these modules? What program do you have? Have you looked at these modules' documentation to see if they have the features you need?
I'm not an user of any of these modules, but looking at their documentation, features, dates of release and such, I ...
Have you considered sticking with Markdown for your actual documentation and adding a POD module to pandoc or to Sphinx to generate your POD files.
written in Perl; No
Free Software; Yes
able to convert multiple POD or Markdown files to multiple HTML files where each HTML file includes a complete index of all files. Yes
The order in the file index included ...
Geany contains several of the features you wanted. It definitely has syntax highlighting, ability to run, and function lists. I've never used the autocomplete, but it claims to have it, and I'm not sure about debugging. It may also have the comment highlighting issue, but I don't know for sure.