Is there a way for survey takers to add rows/columns to questions with multiple answers for different categories?
When you add questions to a survey, you are also building an underlying database that will be used to collect responses to those questions. There are no controls or functions available that would allow survey respondents to manipulate this database, so it is not possible for them to add rows or columns to a questions.
You could add multiple OTHER rows to grid type questions. Or you could use logic to trigger the appearance of additional rows – http://help.surveygizmo.com/help/article/link/setup-question-logic#show-hide-rows-of-a-grid-question. Or you could enable the COMMENT field for the appropriate questions to collect any additional information.
Basically, you will have to build the survey with all of the additional columns and rows, and then use logic to make them available to the respondents.