• PAUSE account: Yes, you will use the same account.
• Name space:I agree (though it's a matter of opinion) that Games::Sudoku::Trainer is better. Nobody owns the Games::Sudoku::* hierarchy, so you don't need to worry about author permission or namespace clashing, from what I can tell. If you want more advice on naming, join and send an email to the module-authors@perl.org mailing list. (On second thought, as I see later on in your post, perhaps App::Games::Sudoku::Trainer.
• Versions: If you're talking about dependency version numbers, you may want to install a clean perlbrew Perl version 5.8.9 (for example), and then try installing your app. Also check the Changes file for each of your dependencies to see if you're using some feature, or relying on some bugfix that didn't show up until later in the module's life.
• Doku: It doesn't hurt to put some boilerplate POD in each module referring the user to the primary documentation, as well as mentioning the license and author.

One more piece of advice. First, upload it with a "developer's version number" (see perlmodstyle for details). Then watch the CPAN testers reports for a week, and see if it fails under any older versions of Perl that you wish to support. Resolve those issues, and then upload with a full-release version number.

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