B4J Question How to launch an external .exe and monitor it...

See jShell library.

you can use tasklist with jShell to see if it's running.

tasklist /fi "imagename eq java.exe"

problem is that something writting in B4J runs under the java.exe so it's hard to identify which process is what so you'll have to check on the window title name.
The same goes for other programs that might start something in the background and close their opening program.

The ProcessCompleted event will be raised when the program ends.

yes, but only if his own app has started the exe AND if the exe doesn't start another process without waiting for it.

if he wants to start his checker every 15 minutes via a scheduled task to see if it still runs he can't rely on the processCompleted event.

if he uses a timer inside his checker app (and keeps the checker app running) he can rely on the processcompleted event but he still needs to check on start if the exe is not already running to prevent misery.