Changing
RewriteRule ^index.html$ http://mywebsite.com/index.php [L]
RewriteRule ^gasterbuch.html$ http://mywebsite.com/guestbook-list.php
RewriteRule ^eintrag-hinzufugen.html$ http://mywebsite.com/guestbook-add.php
to
RewriteRule ^index.html$ /index.php [L]
RewriteRule ^gasterbuch.html$ /guestbook-list.php [L]
RewriteRule ^eintrag-hinzufugen.html$ /guestbook-add.php [L]
should work.