You can bring a tax free quota into Sweden (and many other places for that matter) but you can’t buy tax free inside Sweden, can you?
Airports often have duty free shops just inside customs, so you technically might be able to on a return trip.
Yes, this is possible and legal in Sweden.
The other way to obtain cheap alcohol is to take a cruise via the island of Åland, which is not in the EU. If you plan to visit Åland, make sure to pick a ferry that actually stops there as opposed to just symbolically tossing out a mooring rope for a few minutes to satisfy the legal requirements.