Do we need cash for the bus from the Bergen airport into town, or do they accept credit cards?
They accept credit cards. You can also download the app and buy the tickets on that. (It's cheaper in advance on the app.)
You'll find few places in Norway that don't accept credit cards.
Apart from the bus, the tram can also be a good option. Depending on where in Bergen you are going.
If we purchase advance tickets and our flight is delayed, can they be used on another bus the same day? What is a "period" ticket (says it's available on the route but it's several hundred NOK more).
Take the tram. It goes directly from the airport to city center every 5-10 minutes for about 4 dollars. You can by a ticket from the machine at the stop.
I would only take the airport bus if you are going to the northern side of Bergen -- the area called Åsane.