How to enable that template content headers is linkable? (in "add new item" section)
I don't think this is possible, but raises a good point - perhaps the editor should allow for links here, just as the <$description$> tag allows.
If you mean the title tag you'd actually just want to add the link='true' variable to it and you'll have the option to add a link to your title or not.
<$title link='true' default='Enter Title Here'$>