Questions about BRepAdaptor_Curve usage

Hi all,
I am building my own hobby geometric modeller (with its own C++ data structure representations) and wish to use OpenCascade 7.4.0 API's to perform booleans (and probably fillets/blends in the future). So I convert my classes to equivalent OCC classes, invoke the Boolean api, and then
need to convert resultant Topology/Geometry representation of Opencascade into my own datastructures.
Specifically - I am using BRepAdaptor_Curve class to get underlying geometry curve of the TopoDS_Edge (this is while 'walking through' the topology of the resultant cut body).
Have following questions:-
a) I noticed that BRepAdaptor returns gp_Elips/gp_Circ (if the underlying geometry is indeed elliptic/circular in nature) - but gp_Elips/gp_Circ seems to represent only full ellipse/full circle (this is understanding i get from the documentation).
What if the resultant edge was an elliptic arc or circular arc ? How do I come to know that - Am I supposed to use IsClosed() method (and if false, meaning its an open arc) - then to convert resultant arc into ellipse/circle arc using GC_MakeArcOfEllipse/GC_MakeArcOfCircle constructors?

b) I iterate through the TopoDS_Edges of all the face (in order) using BRepTools_WireExplorer.
So when I use BRepAdaptorCurve to get the geometry of TopoDS_Edge (which is the edge of some face) - then which form of the adapter constructor to use? BRep_AdaptorCurve(TopoDS_Edge& ) or BRep_AdaptorCurve(TopoDS&, Face&)?

Any clarification on the above would be appreciated.

Regards,
Sanjeev.