What fields need to be on Gift Aid declaration form to avoid uncaught exception?
If you miss out required fields it should show you an user-freindly error, not throw an exception. It should also indicate what fields are required. So whether or not the required fields have been entered, this is a bug in the gift aid module.

You can raise it with the developers of the gift aid module. They have an active issues queue here https://github.com/compucorp/uk.co.compucorp.civicrm.giftaid/issues

Regarding scheduled jobs - did you get it working? If so, I recommend updating their documentation and issuing a pull request.