That's not possible right now. The custom profiles created from curves are saved in the document but there is no option available to edit them afterwards. You need to create new profiles if you want to modify some one. We'll try to improve that in future versions.
Regarding your second question, that is not possible either. But it is a good suggestion also for the future development.
Thanks, I mean that would be enough to delete the older version of profile and create a new one. Also a short list would be useful same like in case of wall, beam etc styles where renaming object is easy.