Using the API currently, it is not possible to change any of the parameter values of the existing elements inside a Group, directly. Neither are there any current parameters that are writeable on elements which are part of Groups.
To store some additional information on elements that are part of a group, we can programmatically ungroup a group, add the desired information on all the elements (or the elements you wish to add to) by working on the parameter value and then regroup the elements to form a group again. If any information is meant to be added directly to a Group element, the Group.SetEntity() method could be used to add information to the entire Group element.