Q) What we require is; when the caller reaches this agent group they are passed around to each currently logged in agent for approx 10-15 seconds each. When the caller is passed onto another agent, the prior agents phone stops ringing (instead of all ringing at once). If an agent is not logged in/is already on a call it should simply call another randomly logged in agent.
Ans) Yes, they will all ring one after another, that is how the Agent Group works. If you want everyone to ring at once and if you need separate stages for each set of extension then please try Hunt groups. Its far simpler for you and you can transfer the call from Hunt group to Agent group too (if HG alone, cant solve your query). In short, you dont need to create these many agent groups or any other group. That's the main reason it was created for.