nginx прозрачный обратный прокси - 403, 404 и больше

Two things: you should not use the version shiped with debian. Mine was eating cookies, which took me half a day to figure out. Use the latest debian package supplied by the nginx folks. They supply a repo, so its quite convenient.

For the redirect: I see you are using proxy_redirect off;. Try something like

proxy_redirect http://$host/index.php?page=home http://$host/page/home.html;