Well, they can have the same deal that Norway or Switzerland have with the EU. The problem is that to have that deal they have to agree to be part of Shengen Area
2. It is quite possible to opt out of EU regulations while part of the EEA. But the Norwegian government do not have the balls to do so.
3. Norway had an older agreement with Denmark and Sweden about passport-free travel. It was not Shengen compatible. So either Norway had to join Shengen, or Norwegians had to get used to getting passports to visit said nations.