When you make a local copy of the online extract are you creating a new TDE with all the data again everytime?
Yes, you are creating a copy of the TDE on your local computer.
Are the calculated fields that you create in your workbook a part of the workbook or the datasource(tde)
If you connect to a published data source, but you create a new calculated field in your workbook, the calculated field you just created is a part of your workbook, but not of the published data source, unless you republish the data source specifically.
If you want to add new calculated fields, you can just create them in your workbook and republish the data source without first making a copy. But if you want to modify existing fields, there is no better way I know of than the way you are currently doing it.