re: "Does the application take screenshots?"
Yes.
re: "If you need to leave, you need to suspend?"
Yes.
Just stop the time-tracking application when you stop working on the project.
Think to yourself:
"Hmm... I've been working on this for an hour. I need to break for lunch... I'll stop the time-tracker application now and when I come back, I'll start it again when I resume work."