They still make the news so they can't be that common. Muggings are still relatively rare. Burglaries are a royal pain in parts of the bigger cities. The apartment block I live in has had the basement done about a dozen times in 24 months. I have also been the victim of another popular past time- bicycle theft.
Most crimes seem to be of the economic kind so Sweden is still a pretty safe country to live in.
Visas European citizens do not need a visa or work permit. As with all EU member states a residence permit is a necessity. I am trying to find info. Unless, that is, you have a very rich family. For a cheaper alternative visit a pizza house.