They would have held another one every two years or so until getting the "correct" result. The Swedish gouvernment tried just that, when Euro referendum failed to pass and only stopped once the Greek crisis broke out.
The Swedish Euro referendum was in 2003, and the Greek crisis started in 2009. Plenty of time to "correct the result" as you put it if they wanted; I think it's rather more likely the Govt wanted to join the Euro, and parked the referendum until such a time later when it thought it could realistically win. Which literally every Govt on the planet does. Look at Scotland; lost a fully democratic independence referendum only 5 years ago, already pushing for another one.
Agreed. Sweden would likely have remained in EFTA and the EEA and enhanced Nordic cooperation across EFTA and the EU. I don't see them attempting to get the EU customs union extended to include themselves (because that would be incompatible with their EFTA membership unless they got a derogation from that), but a customs security agreement like what Norway has with the EU (which allows for simplified checks) and a mirroring of the EU's tariffs in most areas seems very likley.
The only reason I mention a Customs Union (which I'm sure EFTA/EU could work out if Sweden/Norway & the EU wanted given that Sweden & Norway would be the only large countries left in EFTA I think by that point) as the business lobby was the main push for the Swedish EU membership effort. The likes of Volvo etc not only want free trade to European markets, but customs free to enable better supply chain efforts and ease of trade. I don't know if it's likely, but I think a "current status + customs union" - the EU signed a customs union with Turkey at about the same time when Turkey looked a good future bet, so I wouldn't rule out the EU being happy to arrange a customs union with EEA Sweden & Norway.
WI both Finland and Sweden voted no.
Relations towards Norway would be as usuall. The movement over the Oresund and Baltic would be propblem as the Nordic toll union would not work anymore and Denmark would be forced to implement a passport zone towards Sweden and Norway as they would not be part of Schengen. Same with Sweden and Finland. The stricter rules for travel would mean that the ferry industry takes a hit since less would travel between Stockholm and Helsinki.
I Think the Oresund brigde would be delayed until things were more clear about passport and freedom of movement.
The Nordic Passport Union dates back to the 1950s; Sweden and Denmark (and Finland and Norway, and later Iceland) have enjoyed passport-free travel since, and so that wouldn't stand in the way of the Oresund Bridge - although customs checks might do if no customs union is agreed (although that doesn't stand significantly in the way of Sweden-Norway OTL traffic).
Schengen was OTL a enhanced co-operation mechanism, not EU law. So Denmark can't be forced to drop the NPU and join Schengen, nor even when it becomes EU law. See the UK & Ireland - EU member states (*cough* currently *cough cough*), who are not part of the Schengen Area at all. If the 3 Scandinavian states don't join Schengen, you can sure bet Finland won't do. OTL none of the Nordic states joined Schengen piecemeal; they all agreed to merge the NPU into Schengen together and at the same time (although I believe the NPU is technically still valid, and grants a few extra rights to intra-Nordic travel & Nordic citizens).
