Can I convert one type of fillable-field into another type of fillable-field: for instance a text-field into a signature field or Initials?

You can't change one type of fillable-field into another, but what you can do is place an API PUT call with a set of fillable fields in JSON format - with the correct types. These fields will override/replace the fields that were initially in the document. Please refer to documentation for the exact format of the API call.