So I am trying to copy a set of data in one column and paste it in a column in another database. Each database has multiple independent columns.
I think you are asking if you can copy/paste a range of cells the way you can in Excel. Sorry, you can't do that in Toad. You have to do one cell at a time.
You need to select the rowid in the table that you are pasting into. So, in the Editor, the query needs to be something like "select t.*, t.rowid from mytable t" or as a shortcut you can just do "edit mytable". Run that with F9 (not F5). Or you can just find the table in the schema browser, then go to the Data tab on the right.