Yes you can, but keep yourself updated about possible changes.
Yes you can. More information at www.migrationsverket.se
Please look at www.arbetsformedlingen.se
For registration contact Skatteverket , Swedish Tax Authority at www.skatteverket.se
No, if you have not worked in Sweden you do not have any right to receive social assistance.
You have the same rights as every citizen in EU, but you have to have money to support yourself, and you have to find a job within 90 days after your arrival.