I would like to combine all attributes into one field and also have it include the field name.
You have posted this in the ArcGIS Python API ... by chance do you want to do this to go to the Python place? or are you interested in Managing Data perhaps?
And you indicate that you want to do this in the field calculator as well. Do you have an example of how you do this now... because you normally provide the field name or names in a field calculator expression. Perhaps you could elaborate on the result you are after to help guide further discussion.
Although you are asking about the field calculator for doing this, have you thought about exporting all the data to a comma delimited .csv or excel file....doing a little manipulations there and then joining the attribute table back? If this is a one shot deal, that may be more straight forward. The hard part you may have is if they are not fixed length, how will you use the data in the fields. This may not be important for your purposes, but without more explain atin it will be hard to give much more advice.
as Dan mentioned, you have this in the Python API geonet space...is that what you are trying to use? If not, you may want to try Moving Content to move it to a a different community on geonet. Since this is from a few weeks ago, if it it resolved, please mark it as assumed answered....and a summary would be nice. If still an issu, please provide more detail.
Retrieving data ...