Hi,
Assigning to groups is not possible and should not be. Use CandidateGroups to make sure, every user of the group has the task in his tasklist and can work on it.
Activiti makes no difference between an assigned task and a 'in work' task. If you have your own frontend, you could combine the claiming & the opening of the taskform so there would be no extra click to only assign the task.
Regards.