ipMonitor doesn't do rights/login/authentication with linux machines. What you can do is to setup a external script that logs into a linux machine and checks some value, and you can have ipmonitor check to see that the value doesn't change. Support had directions on how to do this. As for the http monitor, I don't see why that wouldn't work.
Another idea for monitoring mysql would be to code up a page that runs some transactions against it, then check that page with a standard http monitor.