I've never seen a supermarket in the airport. There's a bunch of little convenience stores, but that's about it (unless there's something out in the grounds).

However, there's no shortage of small supermarkets across the city, varying in price and quality from the likes of Netto up to Irma.

If you want to watch ships, you could head out to Dragor (hard to pronounce!) which is at the back of the airport (easy bus ride). It's a really pleasant little seaside town, with great views out towards the Oresund bridge, the Oresund itself, and the airport. Best is if you can hire a bike and cycle along the coastal path from the airport.