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== My header-buddypress.php: starts with include ( ‘header.php’ ); then some html tag, no php ==

And therein lays the answer to the strange behavior. What hnla said above. header.php is a special template file which is not meant to be included in another file except via get_header call. To resolve your issue, create header-buddypress.php the way I mentioned above. Do the same for your footer-buddypress.php, footer.php is another special file which should only be called via get_footer()