I cannot use the edit or other function even I paid.

Reader is not a PDF editing application.  It is free and excellent. There would not be a trial period for Reader.  To edit PDFs, one should use the full-blown (paid) app Acrobat Pro DC.  Be sure to run Acrobat Pro DC for your PDF editing, and also ensure you are logged into your Adobe account.  This will verify your paid account (or trial period).  Once in the right application, you should have the full complement of editing tools in hand.

Can you confirm (in the title bar across the top of your application) which Adobe tool you are using>?  Is it Reader?  Acrobat Pro DC?  I would maybe restart your computer and launch the app again to see if that dialog box will be dismissed.

Dave