how do I export a student's parents' job title and organisation?

It looks like those fields should be available under the Organisation node that's within the individual relationship section (not the other organisation node further down, as that will give you the constituent's organisation relationships, not the parent's). It's a couple of rows below where you got the phone number fields from.

Odd… are the parents also constituents? Only constituents can have relationship records associated with them, so if the parents only exist as relationships on the child's record, they can't have their own employment information associated with them.

If it's not that, you may need to select which types of organisation relationships you're exporting - if you've currently got the criteria set to “all organisation relations” then maybe try toggling it to “selected organisation relations” and then choosing the relationship type(s) that you use for employment.

If the parents have their own constituent record you should be able to pull Relationship Individual →Organization.

I would suggest flipping the script. Assuming parents have their own constituent record.

Pull a query of parents through Export and have the output fields be the parent employer info and all of their children. You'd be able to see who is current student by the grad year minimally, depending on what else you track.