Is it possible to send additional fields to Square - Like a transaction number and some detail field(s)?

Unfortunately it is currently not possible to send additional fields to Square. If you want to have transaction number or other details, you can only collect them directly on the form itself by adding a Unique ID widget or textbox fields. However you will not be able to pass the details on this field into Square.

Please let us know if you need further assistance.
Regards.