Android is based on Linux; can native Linux applications be run on Android?
Yes you can. I have installed a complete Debian distribution in a chroot-jail enviroment using debootstrap. (You need a rooted device) I am now running ssh, apache, mysql, php and even a samba server under android on my htc-desire with no problems. It is possible to run x applications using a remote x server via ssh. It even runs openoffice.org and firefox. You can use this: http://code.google.com/p/android-xserver/ to run X-application on localhost but my HTC-desire has a to small screen to be productive :-) But it might be usefull on a Eee Pad Transformer or something like that.