Possible to re-use one field multiple times in a section?
You can re-use the same text field multiple times in a section on different Entry Types, but if you would like to re-use the same text field multiple times on the same Entry Type (or page) your best bet would be to make it a Matrix Block. 

For a quick overview on Matrix Blocks: https://craftcms.com/features/matrix

More info on Matrix Blocks: https://craftcms.com/docs/matrix-fields