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How can I change the place of the subscription checkbox?

Use this code (within the loop) in your template file, to change the place of the checkbox: <?php show_subscription_checkbox(); ?>

Can people subscribe manually without commenting?

Yes, just place this code snippet in your template (outside the comments form): <?php show_manual_subscription_form(); ?>

I use Hosteurope and I cannot send e-mails via this plugin

See this comment for a solution: http://www.sjmp.de/internet/subscribe-to-comments-mit-double-opt-in-pruefung/comment-page-10/#comment-4460