Privoxy is your missing piece. Combine that with OpenVPN.
For compression: http://www.privoxy.org/user-manual/config.html#ENABLE-COMPRE...
edit: Also, setting proxies on Android -- http://w3epic.com/how-to-setting-proxy-on-android-phone-tabl... ... iPhone: http://appletoolbox.com/2012/08/how-to-set-up-and-configure-...