To get to the run display, you push your device's "action button" in and hold down your stylus on the clock. If you have any programs like WISbar running you need to close them first so you can see the real title bar. I think on your ipaq the action button means pushing in the D-pad thing on the front. Just like the desktop version of quake, you can start maps and mods from the command line.
A much easier way is to use PocketQuake launcher.
Get it . It lets you run maps and mods without much trouble.
To stop the demos from playing, get a PAK editor (one is found ), open up the pak0.pak file from your pocketPc (if it is gzipped you need to un-gzip it first, use winzip). Next delete the .dem files that are inside the pak file.
For more information about Quake 1, look here:
http://www.planetquake.com/quake1/