We arrive at 9am Thursday at Geneva airport. I've tried buying tickets online but a few different sites have not been able to complete the sale.
Can I buy tickets at Geneva airport to Fiesch via Brig and how straight forward is this?
I don't see any reason why you wouldn't be able to. There are both ticket machines and manned positions in the Geneva Airport train station. As long as you have cash or an acceptable card it should be quite straightforward.
There are two trains an hour, so even if you have to wait in line a bit it shouldn't be an issue.
However, I don't see a reason either for not being able to buy the tickets online. Have you tried sbb.ch?