Is it possible to put Geoserver behind a proxy and access the WMS/WFS using OpenLayers

You can have an apache httpd as frontend listening on port 80 with proyxing rewrite-rules (see mod_rewrite and mod_proxy) mapping /whateverurl on apache to /geoserver/wms on the geoserver running on another tcp port.

Se more: http://httpd.apache.org/docs/2.0/mod/mod_rewrite.html