I am unable to export the submitted answers for the extended text category questions. I can view the submitted answers by the user in Gradebook however unable to export it.

Are you able to export any other category questions?

Nopes, unable to export any answers

I'm afraid there's no massive export function for that.
It can be developed, indeed.

I'd love to know how to export test answers within a course. I speak SQL - is there a way to pull this information from a table somewhere? (with hundreds of users we'd like to download their answers to items and not click through each one).

You can surely do with SQL.
If you need help with that, you can contact me in private.