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I like your thinking: use MapInfo Pro to create the MapBasic code for you. That's probably the way many of us started when we wanted to learn MapBasic.
Adding columns can be done using the Table Structure that you can access via the context menu on the table in the Table List or from the Table dropdown in the Maintenance group on the TABLE tab.
This is the MapBasic code you are looking for:
Alter Table MyTable (Add Latitude Float, Longitude Float)
Set CoordSys Earth Projection 1, 104
Update MyTable Set Latitude = CentroidY(obj), Longitude = CentroidX(obj)
Note that the first statement will fail if the columns already exist.
PS: If you are doing this with MapInfo Pro v2019, you can use the new SQL Window and save it to a MapBasic script, a new file format we just added.