Embassy of sweden Zagreb, Croatia

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

Please check the following website to check if you need a visa for Sweden:
Visa for entry to Sweden

In case you need a visa please apply at the Embassy of Norway in Zagreb.

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.

Yes, but check the regulations at http://www.jordbruksverket.se/swedishboardofagriculture/engelskasidor/animals/import/dogscatsandferrets.4.295b2341134f64e5d6280001001.html