The answer to the question “How do I do x in eggPlant?” is almost always, “How would a user do x?” As a user, it sounds like you open the Start menu and look for the 3 separate processes, so that’s what your script would do:
TypeText windowsKey // open the Start menu
WaitForAll 10, "process1", "process2", "process3"
This is one approach; if any of the processes aren’t found, then the script will just fail. You could also do something like this:
if not imageFound("process1") then
-- do what is needed to launch process1
if not imageFound("process2")? // etc.
The same answer applies to your first question – how do you as a user determine whether an application is running? There aren’t really any shortcuts in eggPlant scripting other than those provided by the OS/application being tested. So you could have eggPlant look for the application in the Start menu or in the Task Bar or if you expect it to be up and running, you can just look for some element of the application’s UI.