if you leave it going every minute then it will eat up your bandwidth.
but that also depends on the size of the file you are requesting.
make a simle HTML file with one charector in it, and make another script to request that file, or log an error mesage...
that way you'll only be downloadin 8 bytes, and your bandwidth will be relativly untouched.
also yes, you have to host the thing that check the uptime somewhere else, and if the server that host the uptime monitor goes down this will affect your uptime results.
why don't you just use www.netcraft.com