Hello!

I'm coming to Copenhagen for a week of work but will be staying in Malmo and commuting back and forth daily. (The hotels in Copenhagen were either completely booked or frightfully expensive.) The Jojo Sommar card and Oresund trains seem like the simplest way to make that commute, but I had some questions about the card:

• Does the Jojo Sommar card cover trips on Oresund trains into Denmark (i.e. Copenhagen airport and Copenhagen's central station)?
  On the Skanetrafiken Web site, the headline says "Jojo Sommar covers unlimited travel on buses and trains within Skåne in the period 15 June-15 August." But further down the page, it says it is valid on all Oresund trains. Which prevails -- the "within Skane", or "all Oresund trains", which would presumably include trains to Copenhagen airport and into Copenhagen?
• Can this card be purchased at red Skanetrafiken ticket machines in Copenhagen airport, or can it only be purchased in Malmo at the central station (or from some other ticket office in Sweden)?
• Will I need a separate card for Copenhagen public transport? (Presumably yes, if I ride anything besides Oresund trains...)

Thanks in advance!