The ban last for a full seven days, therefore, for example, if you left the group after the finals at 9.30pm, your ban will be lifted on the next Saturday, 9.30pm. (After next week's finals) Therefore, you will only be able to participate after waiting for one whole week.
As for the group, as long as you ac*ulate 200 activity rate, you should be able to participate. I am not sure about this though.